"Free will" or just 'will' ?

You cannot always choose - conscious choice implies awareness: but when you can, choose well.

Free will has been the subject of argument in Western philosophy: partly because of notions like "God is omnipotent" (because if God can do anything and does everything then how much choice do we have); and/or because the opposite notion of the world having a physical (not spiritual or mental) basis.

IMO this is a 'false dichotomy'. It might be asking a question about the existence of self of the kind that it's recommended you don't ask.

There was a nursery story (i.e. a children's fable) told to me: someone asked a centipede, "Which foot do you move first?" and the centipede thought about it and didn't know and got confused etc. Whereas a natural centipede will just move.

Similarly a natural person makes decisions, and those decisions have an effect, and self-training (if you choose to do so) can make the decisions more skillful, etc.

Words are pointers. They are not the thing they represent. As such the question misses the point.

In Buddhism there a distinction between karma and things like cultural programming on the one hand and liberation and conscious choice on the other hand.

The problem is that you don't have a concept of what conscious choice means. You might never have experienced it so any word can't point you to the concept. You will always match it to previous experience that are of a different quality. You can observe that all the decisions you have made in your life can't be reasonably called free but that doesn't mean that's true for everyone.

If you sit a while in meditation you can discover new ways to make choices. Not anymore by bound to pick the chocolate because you have aren't picking the chocolate anymore because you have a craving for it or eat the apple because you should eat healthy.

There may be a mistake in your first sentence, i.e.:

The term "free will" can imply that one's will is without causes.

I think that the state of willing (wanting) anything "without cause" or "for no reason" would (if that state can even exist at all) be seen as a bad (unnecessary, useless, random, insane, unwise) thing.

If that (madness) were the actual definition of "free will", then probably nobody would be interested in it.

Instead of "without cause", the first two sentences in Wikipedia say "unimpeded by contraints",

Free will is the ability of agents to make choices unimpeded by certain prevailing factors. Such prevailing factors that have been studied in the past have included metaphysical constraints (such as logical, nomological, or theological determinism),[1] physical constraints (such as chains or imprisonment), social constraints (such as threat of punishment or censure), and mental constraints (such as compulsions or phobias, neurological disorders, or genetic predispositions).

For example:

• A "prevailing factor" might be that my neighbour owns something which I do not own and which I want: but "unimpeded" by that factor I might be able to "freely choose" to not steal it.

• A "constraint" might be that I'm hungry and have no food: but unimpeded by that constraint I might "freely choose" to be happy instead.

• A "constraint" might be that my country's laws require me to join the army and go to war: but unimpeded by that constraint I might "freely choose" to go to prison instead.

• A "constraint" might be that you are taking (stealing) things from my house, but unimpeded by that constraint I might "freely choose" to give those things to you as a gift.

Some things (e.g. a river which is running downstream) might be seen as acting mechanically without having any "will" (and without sentience): they're just a machine.

• Part of the "free will" discussion is whether people have no choice because things are pre-decided by God.

• Another part of the "free will" discussion is whether people have no choice because things are pre-decided by Physics, by a nothing-but-mechanical nature/universe.

I suspect that by the time you agree or claim that there is such a thing as "will" and "choice", then you're already moving away from Hard determinism.

I searched the Wikipedia article to see whether it mentions such a thing as non-free will. The word "will" exists 500 times in the article, and almost every time it's used it's used with the word "free". In other words, "will" and "free will" might be (intended to be) used as synonyms: if it's not "free" then it's not "will".

For example if you a enter a contract under duress then the contract can be void: because if it wasn't of your own "free" will, therefore it wasn't really "your will" at all.

There only very few (pathological) places in the Wikipedia article where "will" is used without "free":

Free will as a psychological state

A person's will is identified with their effective first-order desire, that is, the one they act on, and this will is free if it was the desire the person wanted to act upon, that is, the person's second-order desire was effective. So, for example, there are "wanton addicts", "unwilling addicts" and "willing addicts". All three groups may have the conflicting first-order desires to want to take the drug they are addicted to and to not want to take it. The first group, wanton addicts, have no second-order desire not to take the drug. The second group, "unwilling addicts", have a second-order desire not to take the drug, while the third group, "willing addicts", have a second-order desire to take it. According to Frankfurt, the members of the first group are devoid of will and therefore are no longer persons. The members of the second group freely desire not to take the drug, but their will is overcome by the addiction. Finally, the members of the third group willingly take the drug they are addicted to.

and

The physical mind (see also Neuroscience of free will)

For example, an addict may experience a conscious desire to escape addiction, but be unable to do so. The "will" is disconnected from the freedom to act.

and

Neurology and psychiatry

Similarly, one of the most important ("first rank") diagnostic symptoms of schizophrenia is the delusion of being controlled by an external force.[186] People with schizophrenia will sometimes report that, although they are acting in the world, they did not initiate, or will, the particular actions they performed. This is sometimes likened to being a robot controlled by someone else. Although the neural mechanisms of schizophrenia are not yet clear, one influential hypothesis is that there is a breakdown in brain systems that compare motor commands with the feedback received from the body (known as proprioception), leading to attendant hallucinations and delusions of control.[187]

I suspect you'll agree that Buddhists commonly experience at least the first kind of "freedom": the feeling that they are able to do what they want to do.

Note however that being conscious that "I choose" might be a view of self. An answer like this one might (I don't know) suggest that "free will" and "choosing" is the normal state of mind: and that a state of non-choosing or surrender-of-self might be an (enlightened) ideal which a Buddhist aims for.

The ego has survival instincts hardwired into our bodies. These survival tendencies are what give rise to greed, ignorance and hatred. This is what creates suffering.

To be conscious of this process is the aim of most Buddhist paths. This awareness itself is what gives rise to our capacity to choose something other than what our programming demands. Thus, "free will" as opposed to "will". Will implies that our choices are predetermined, which is true when the ego reigns.

Free will is the entire point of our chasing enlightenment to begin with. This is why Buddhism exists, and why it's called "liberation" in English.