Outside the technical definition, what is the term "Pharisee" synomynous with inside Christian Teachings?

Since you asked for the non-technical definition, I'd say:

Primarily: hypocritical, legalistic, self-righteous, "puffed up with knowledge /doctrine"

Secondarily: haughty, proud, hard-hearted, traditionalist, fundamentalist

The Pharisees were famous for having all of the outward trappings of holiness and peity and for meticulously following the law while being inwardly spiritually devoid ( "white washed tombs"). You could say they were excellent at keeping the letter of the law while completely missing its spirit. Biblical examples include praying in public to appear devout or tithing large amounts in a public manner in order to appear generous and holy. (godly actions, ungodly motivations)

Also, in very rough terms, the Pharisees were known for being the fundamentalist, traditional, conservative, legalistic group of their time (as opposed to the Sadducees which were more liberal, non-traditional, ect.).

So, when used in the modern context, the term Pharisee usually refers to a combination of both the negative (eg self righteous) and more neutral (eg fundamentalist) aspects mentioned above.

If we want to get really informal: stuck-up, rulsey, self-righteous person who is great at following the rules while completely missing their point.

Outside the technical definition, what is the term "Pharisee" synomynous with inside Christian Teachings?

We amost all know what a Pharisee is! In Judaism, a Pharisee is a member of an ancient Jewish sect that was opposed to the Sadducees, teaching strict observance of Jewish tradition as interpreted rabbinically and believing in life after death.

However after Our Lord recounted the parable about the Pharisee and the Publican, Christians have given it a secondary meaning: a self-righteous or hypocritical person.

We can easily see that the Pharisee actually a hypocrite and prides himself in what he does and that he is not like other repentant sinners: humble.

The Parable of the Pharisee and the Tax Collector

9 To some who were confident of their own righteousness and looked down on everyone else, Jesus told this parable: 10 “Two men went up to the temple to pray, one a Pharisee and the other a tax collector. 11 The Pharisee stood by himself and prayed: ‘God, I thank you that I am not like other people—robbers, evildoers, adulterers—or even like this tax collector. 12 I fast twice a week and give a tenth of all I get.’

13 “But the tax collector stood at a distance. He would not even look up to heaven, but beat his breast and said, ‘God, have mercy on me, a sinner.’

14 “I tell you that this man, rather than the other, went home justified before God. For all those who exalt themselves will be humbled, and those who humble themselves will be exalted.” - Luke 18:9-14

Thus we have two basic definitions of what a Pharisee is!

Pharisee

1. Judaism

• a member of an ancient Jewish sect that was opposed to the Sadducees, teaching strict observance of Jewish tradition as interpreted rabbinically and believing in life after death and in the coming of the Messiah

2. (often not capital)

• a self-righteous or hypocritical person

The OP's term "inside Christian teachings" raises problems because the Pharisees are portrayed in various ways in the Bible and in Christian tradition. Most of us know of the negative qualities usually associated with Pharisaism--legalism, hypocrisy, intolerance, self-righteousness, hard-heartedness, etc. Fewer Christians are aware of the positive characteristics of Pharisaism and individual Pharisees in the Bible and Christian teachings.

Today, Christian scholars have begun to correct the one-sided characterization of Pharisees in Christian tradition. For example, Dr. Joseph Sievers of the Biblical Pontifical Institute has teamed up with Jewish scholar Amy-Jill Levine to produce The Pharisees, described as "a multidisciplinary appraisal of who the Pharisees actually were, what they believed and taught, and how they have been depicted throughout history." Meanwhile Protestant professor Kent L. Yinger of George Fox University has written a book with the same title which "challenges [us] to re-read the gospel stories with real Pharisees in mind rather than caricatures."

With this in mind, here are some biblical facts that Christians often overlook:

• Pharisees could be broad-minded.

Hillel the Elder, the greatest Pharisee of the generation prior to Jesus, gladly taught gentiles as well as Jews, famously declaring "Do not unto others what is hateful to you." His grandson, Gamaliel I, later defended the leaders of the Early Church in the Book of Acts.

• Pharisees taught the Golden Rule.

And behold, a lawyer stood up to put him to the test, saying, “Teacher, what shall I do to inherit eternal life?” He said to him, “What is written in the law? How do you read?” And he answered, “You shall love the Lord your God with all your heart, and with all your soul, and with all your strength, and with all your mind; and your neighbor as yourself.” (Luke 10:25-27)

• Pharisees agreed with Jesus and Paul on the doctrine of the Resurrection. (Acts 23)

• A Pharisee (Nicodemus) defended Jesus in the Sanhedrin.

Nicode′mus, who had gone to him before, and who was one of them [the Pharisees], said to them, “Does our law judge a man without first giving him a hearing and learning what he does?” (Acts 7:50-51)

• Another Pharisee (Simon of Capernaum) invited Jesus to dine with him as an honored guest. (Luke 7:36)

• Jesus advised his followers to accept the Pharisees' teachings, if not their practice:

The scribes and the Pharisees sit on Moses’ seat; so practice and observe whatever they tell you, but not what they do; for they preach, but do not practice. (Mt. 23:2-3)

• Pharisees warned Jesus that Herod Antipas sought his life (Luke 13:31)

• Pharisees joined the Early Church. (Acts 15:5)

• Paul still identified himself a Pharisee long after he became a Christian.

When Paul perceived that one part were Sad′ducees and the other Pharisees, he cried out in the council, “Brethren, I am a Pharisee, a son of Pharisees. (Acts 23:6)

In addition, we should be aware that one of the characteristics of Pharisaism in Jesus' day was the diversity of opinion among the Pharisees. Adherents of Hillel's school tended to be more broadminded, while those who followed Shammai were more strict. Some of the issues that Jesus debated with "the Pharisees" (hand-washing, association with sinners, healing on the Sabbath etc.) indicate that his opponents were likely members of the "House of Shammai" rather than of Hillel. An exception is Jesus' teaching on divorce, where he agreed more with the strict line of Shammai as opposed to the liberal policy of Hillel. However, on many issues of Jewish law Jesus and the Pharisees had much in common. This may be what lies behind Jesus' admonition to his disciples to "practice and observe whatever they tell you."

Conclusion: The term "Pharisee" generally has negative connotations in Christian tradition. But a closer examination shows that the stereotypical characterization of the Pharisees is unfair. Christian scholarship today has begun to correct this.

The question asks about the usage of the English word 'Pharisee'.

The Oxford English Dictionary has three entries for the English word.

1. 1. A member of a religious party within Judaism between the 2nd cent. B.C. and New Testament times, distinguished by its rigorous interpretation and observance of the written Mosaic law as well as the traditions of the elders

2. 2. A person of the spirit or character commonly attributed to the Pharisees in the New Testament; a legalist or formalist; a self-righteous person, a hypocrite

The third is a specialised use, not related to this subject, which use seems to relate to a regional dialect where 'fairies' is pronounced 'farsies' then 'farisees'.

The second meaning makes it clear that some use the English word 'Pharisee' in common speech to refer to a person who exhibits the characteristics of the Pharisees as reported by Matthew, Mark, Luke and John.

The question states 'incredulous' as one of the characteristics of Pharisees and I agree that unbelief is evident, both in the persons described in the gospel accounts but also in those who exhibit a like spirit today.

And I must confess, that, in regard to certain times in my life, I have to look back and admit, that, yes, I was pharisaical : proud of my religiousness, smug as to my connections and associations, yet not free of my own carnality, wordliness and besetting sins.

Nor am I free yet of such tendencies, for although I cannot say, right this moment, that I am such, yet I know how both nature and flesh and blood tend in that direction unless both grace and mercy, also afflictions and chastis*m*nts, are dealt to me from on high.

The unbelief of the Pharisees, in regard to Jesus and whom he truly was, is evidently a result of them not receiving John the Baptist, nor submitting to the baptism of repentance, Matthew 21: 28 to 46.

Hard of heart, impenitent, assured of their own position, their own rightness and their own inheritance in the future, they rejected John : and thus rejected the Son of man.

Their behaviour is a warning to us all.