In what different ways is the word "cult" used as a label inside Christianity?

Speaking from experience; in general use I would advise against it. It's used more as a curse than a description, as such it does not achieve anything other than anger, seperation, contention and hate.

As a technical description all abrahamic religions (IE christians, jews, and muslims) would fall under the term cult.

People generally associate a negative context with the term cult due to various historical extreme individuals and groups that were cults. Due to this cultural context, the term cult is often used to belittle others rather than to provide an accurate and informative description of them.

IF you think something is evil and needs to be avoided, I would advise to be more specific than just using the term cult.

Dictionary.com - Cult

As one person pointed out, the word is used very broadly, by different people and different groups to denote a religion or sect that is fringe, or radical.

However, there is a more specific answer, and I'll give specific examples that I think will make things much more clear about when Bible teachers, pastors and scholars use it as opposed to someone who doesn't agree with another denomination on a few points and labels them a "cult."

In general, Protestant missionaries and clergy use the term cult, in referring to a religion

• 1. that has or uses another source of scripture or sacred writings in addition to the Bible or special revelation given to their leader or exclusive to their followers.
• 2. denies the deity of Christ or other core tenets such as the virgin birth, etc. Denies that Jesus is God.
     Here's a fantastic article that uses both Christian and secular sources. https://www.xenos.org/essays/what-cult

So Mormons use the Book of Mormon. Also, they deny the deity of Christ. Jehovah's Witnesses have a different Bible and rely very heavily on commentary and articles from the Watchtower. They also deny the Trinity, and reject the deity of Christ. They say he was a created being.

Islam of course is a cult because it uses the Quran, which directly opposes the Bible. It also denies the Trinity and the virgin Birth of Jesus Christ.

So here's an example within Christianity:

One group of Seventh Day Adventist's is considered a cult, while another group of Seventh Day Adventists is a denomination of Evangelical Christianity. So what is it that makes the one branch a cult??
Seventh Day Adventists had a split over the writings of Ellen White, who plagiarized the writings of someone else. They say that they don't consider them on the same level as scripture, but they taught that her writings were inspired - so it's basically the same thing.

The one branch that separated - totally denounces her writings as plagiarism and recognize Ellen White as a false prophet. This group is a denomination within Christianity and the primary difference is that they observe the Sabbath, and have some dietary restrictions, and some of them follow and observe the 7 feasts of the Lord - as they are also "Shabbat". The same Hebrew word "Shabbat" for weekly Sabbath and the seven feasts - Shabbat.

The group which still teaches and follows the writings of Ellen White are considered by many Evangelicals as a cult- because they have this extra "sacred writings".

The following article also gives a good overview: What is the definition of a cult?.

I've always understood "cult" as referring to an abnormal devotion to a specific person, thing, or idea.

This is one of those elliptical words, like "remote", "cash", and "microwave", that are only part of the full expression, "remote control", "cash register", and "microwave oven". Most people today use "cult" to mean "religious cult".

But a cult isn't necessarily a religion; it's enough that its members behave as if it is:

• The fictional world of Harry Potter has a cult following.
• Many entertainment stars have cult followings.
• Some people are fanatics about environmentalism.
• Members of the People's Temple effectively treated Jim Jones as a God.

But note that this fanaticism must also be abnormal:

• Some people believe the Pope is God's representative on Earth, who under certain conditions is capable of making infallible statements.
• Some people believe it is their duty to visit Mecca and circle a sacred rock there.
• Some people believe that cattle represent divine beneficence and should be venerated.

If these were only a few hundred people, they'd be considered cults. But each group has a billion or more members. Their behaviour is normal.

The Latter Day Saints started as a group of people that believed God had given divine revelation to Joseph Smith. That revelation, presented in The Book of Mormon guided their lives. They were a very small group, they no longer fit into mainstream society, and they were directly led by one man (or a small group of men).

It was their size, devotion, and difference from the norm that made them a cult. Today though, they have a following of millions, and most are generally integrated into society, so generally they are no longer considered a cult.

As for "the sense in which the word is able to adapt to apply to both one man whack jobs … as well as larger stable groups", it depends on how the person using it relates to it.

A hard-line Christian would see Roman Catholics as being Christian. Despite doing a few things differently and having a few unnecessary beliefs, they are still seen as fellow Christians, different, but common enough that they can still be considered part of normal society.

That same Christian would see David Koresh's group as being Christian, but would not be able to relate to its members as fellow Christians. The members are few, and behave very differently from how one expects a Christian to behave. They stick out from the crowd and present a bad image of what this person thinks Christianity means.

Seventh Day Adventists share many non-mainstream Christianity beliefs with David Koresh, but they aren't fanatical followers of a charismatic leader and they integrate well into normal society, and so aren't considered a religious cult.

On the other hand, even though there are half a billion Buddhists, they are far less common in Christian countries, and so in some places they can appear to be a religious cult when they don't integrate into society (e.g. wearing orange robes in Smalltown USA).

There is no single definition of "cult". There are several definitions of which I am aware, and I can't say any of them are necessarily more right than any others. Words only have meanings insofar as people agree to give them the meanings that they do. So we can't say one of these definitions is right and the other is wrong. We can just say they are different.

1. Original: in the original sense, "cult" means worship. This sense is sometimes still used, e.g. one speaks of the Roman Catholic "cult of the Virgin Mary". This sense is neither positive or negative in itself, it's neutral.
2. Sociological: a cult is a religious group with a high degree of tension with the surrounding society, and beliefs that are novel for that society. By contrast, a sect has the high tension, but has traditional rather than novel beliefs, and a denomination has neither high tension nor novel beliefs. What is a cult in one society might be a sect in another - thus Hare Krishna are a cult in traditionally Christian countries, but a sect in India. This sense is meant to be neutral - to call something a cult is not to cast judgement on it. According to this sense, Christianity was originally a cult, but is not a cult any longer.
3. Psychological: a cult is a destructive, authoritarian group, e.g. one that uses brainwashing, one that threatens to result in violent acts or mass suicide or so on. This is a negative sense - by calling something a cult, one is suggesting it is wrong, dangerous, and maybe even ought to be prohibited. Maybe sometimes it is justified, but I feel often this is just a way of smearing religious minorities.
4. Theological: in Christianity, "cult" is used to refer to groups that present themselves as having orthodox Christian theology, but in fact are heterodox. So this excludes groups that make no claim to be Christian (e.g. Hare Krishna, Wicca, Satanism, Scientology, Buddhism, etc), but includes groups which claim to be Christian but the user of the term considers to be outside of normative Christianity. So LDS, Jehovah's Witnesses, etc., are commonly included in this group; and some will even add more mainstream groups to this label, such as Roman Catholic or Eastern Orthodox. This is a negative sense. It only really makes sense in the context of intra-Christian discussions; it doesn't make any sense to people who don't identify as Christian.
5. Popular: a "cult" is any purely secular object of adoration and obsession. So Apple is a cult, and Elvis too. This is not necessarily a negative sense, but often is.

Like so many ordinary and common words, cult has a specific meaning in the Catholic Church which sounds weird from the outside.

When a saint is declared a Servant of God by a Bishop, it gives the ok for a local cult to rise up around that holy person. This cult can extend to the entire world once the person is declared venerable.

So, in this case, the cult is the group of people who is asking for the intercession of a particular would-be saint.

If a saint's origin is declared dubious, as some have been in the last century, we say their cult has been supressed.

There are two senses

In the benign sense, a cult is any minority group with shared beliefs or practices that intentionally deviate from the majority. The connotation is one of foreignness and friction with a larger group.

In the malignant sense, the psychological perspective is generally applied, and there actually is set of criteria (a "formula") for determine whether a group is using dishonest (brain-washing) practices to recruit and retain members. A pretty well-accepted list of criteria is summarized on wikipedia:

1. People are put in physically or emotionally distressing situations;
2. Their problems are reduced to one simple explanation, which is repeatedly emphasized;
3. They receive what seems to be unconditional love, acceptance, and attention from a charismatic leader or group;
4. They get a new identity based on the group;
5. They are subject to entrapment (isolation from friends, relatives and the mainstream culture) and their access to information is severely controlled.

Groups that follow the pattern above are very dangerous. Variations of this checklists have been published by various PhD's and psychological groups. One example:

http://www.csj.org/infoserv_cult101/checklis.htm

And an example of how to start a cult, used to illustrate similar criteria:

http://www.psychologytoday.com/blog/look-it-way/200906/how-start-cult

Common to both senses

A "cult" is a deviation from some norm. And, the label can be accurately applied to any type of group, whether the group's focus is on art, film, history, science, religion, etc.. Thus, in both senses, it's clear that a "cult" does not accurately represent the beliefs or practices of the contextual group (the contrasted norm).

There may be "sub-senses" to each sense of the word. But, I believe the two "primary" senses, as I understand them, are sufficient in most cases. And in all cases, it's important to be clear as the speaker/author and request clarification as the listener/reader when the sense is not abundantly obvious.