The Bare Adjective
The Greek adjective πας means "all, the whole, every kind of," depending purely on context. Its different grammatical forms do not change the meaning, and are purely morphological.
The Difficulty of Being Dogmatic
But sometimes determining the intended sense is tricky—you can't come down on either side and dig your heels in, due to the sheer ambiguity inherent in the word, as well as the multiple possible ways of looking at the context as a whole.
Romans 3:23 (DRB) But now without the law the justice of God is made manifest, being witnessed by the law and the prophets. 22 Even the justice of God, by faith of Jesus Christ, unto all and upon all them that believe in him: for there is no distinction: 23 For all have sinned, and do need the glory of God.
Here, in one sense, the "all" answers to "no distinction between kinds of people" (such as Jews and Gentile: Romans 10:13), not 'all men in history.'
In one sense this passage has nothing to do with whether all human beings are sinners, even. Read it about two times if that's not clear. But implied by it is the fact that something underlies the human creature in his present and historical condition which is common to all, namely, a certain 'natural state' (Ephesians 2:3).
Here, a passage commonly cited to prove absolutely all human beings in history have sinned doesn't actually have this in view in this passage: it says "for all have sinned" in answer to "there is no distinction."
So here, there is a fuzzy line between the two senses of the word.
One might argue that Jesus being one obvious exception to "absolutely all men" necessitates we understand this to mean 'all kinds of men without exception are in need of redemption.' (I've also seen this verse used to disprove Mary's being concieved without sin, for example.)
So what about our passage?
1 Timothy 2:1-4 (DRB) I desire therefore, first of all, that supplications, prayers, intercessions, and thanksgivings be made for all men: 2 For kings, and for all that are in high station: that we may lead a quiet and a peaceable life in all piety and chastity. 3 For this is good and acceptable in the sight of God our Saviour, 4 Who will have all men to be saved, and to come to the knowledge of the truth.
There are a few valid ways to take this. Of them, the view that "kings, etc." are included so as make sure these are not exceptions to the universality meant.
Or the view which takes these to be particularly important, practical or relevant examples for a particular persecuted group of people (the Christian community under Roman rule, for instance).
Then there is the view which says "all" in at least the last instance means "all kinds of." This view takes "kings etc." as examples of kinds of people in the group of "all kinds of men," and "For... God desires all" to mean "For God desires all kinds of men, including even these, to be saved."
All are viable understandings. But as demonstrated with the example from Romans 3, it's not easy even when deciding on one to exclude the others. The word "all" is often ambiguous or even multivalent in meaning, which in turn further complicates things by yielding different ways of interpreting 'fors' and 'sinces.'
Something must be acknowledged by both sides of the argument: man's freedom, and the 'openness to all' in these passages, however liberal, cannot be interpreted in a sense which means people could be potentially saved whom God knows in His atemporal knowledge of all things, are not saved and do not receive eternal life.
So even according to the view with the most freedom in man does not necessitate that the "all" ever meant "potentially even those who are not of the elect." And as such, no breach of God's sovereign knowledge of His elect, whom He has chosen, as if they could hop in unnoticed—He knew before the world was created, and His knowledge cannot change.
This cannot be true, since Jesus said:
Matthew 22:14 (DRB) For many are called [to the Wedding Feast of the Lamb], but few are chosen [eklektoi].