In act 1, scene 3 of William Shakespeare's Macbeth, three witches make three prophecies to Macbeth and to Banquo. The major differences between the prophecies made to Macbeth and those made to Banquo are that Macbeth's prophecies are clear and straightforward, whereas Banquo's prophecies are paradoxical and enigmatic.
The truth of the prophecies made to Macbeth is aided by the fact that two of the prophecies are true even before they're told to him. Macbeth is already thane of Glamis and thane of Cawdor before act 1, scene 3 even begins. Macbeth has been thane of Glamis since the death of his father about fifteen years earlier, and Macbeth is made thane of Cawdor by King Duncan in act 1, scene 2.
DUNCAN. Go pronounce his [the thane of Cawdor's] present death,
And with his former title greet Macbeth.
(act 1, scene 2, lines 74–76)
Macbeth's third prophecy, that he "shalt be King hereafter!" actually comes true, although no one can be certain that Macbeth would have become king if he would have let fate take its course, rather than murder Duncan and usurp the throne of Scotland himself.
MACBETH. If chance will have me king, why, chance
may crown me
Without my stir.
(act 1, scene 3, lines 155–157)
The prophecies made to Banquo that he is now, or ever will be, "lesser than Macbeth and greater" and "not so happy, yet much happier" are only partially borne out in the play. Banquo is of equal rank as Macbeth—both are generals in Duncan's army— but a lesser warrior than Macbeth and of better character. Banquo is simply a better person than Macbeth.
It's difficult to explain how Banquo can be happier than Macbeth when Macbeth has Banquo murdered, except for the prophecy to mean that Banquo didn't have to suffer through the remorse, regret, and madness that Macbeth suffers in the play, not to mention being constantly berated by Lady Macbeth.
As far as the prophecy that Banquo "shalt get kings, though thou be none" is concerned, it's true that Banquo doesn't become king, though the prophecy in its entirety doesn't necessarily come true in the play. The three murderers that Macbeth sends to kill Banquo and his son, Fleance, manage only to kill Banquo, and Fleance escapes. Fleance never again appears in the play, and it is Duncan's son, Malcolm, who becomes king, not Fleance.
Shakespeare's subtle references to James I himself—the "two-fold balls and treble scepters"—that Shakespeare interjects into the apparition of the never-ending parade of kings descended from Banquo flatters James I (who believes he is a descendant of Banquo), but none of these descendants ever technically become king within the play.