pusher is just a counter puncher that does not have full strokes (ie. tends to have bunt or push strokes that do not follow through the contact and reduces error by not adding much energy to the shot - ie. they just redirect incoming energy)
the "pusher" stop being called a "pusher" by say 4.5, because everyone at 4.5 swings through the ball (albeit at 4.5+ the "pusher" follow through is long, but the takeback/prep is short).
some folks would call, gilles simon a pro "pusher"... but he's really just a counter puncher, and no one would confuse his strokes with that of a true pusher (eg. short backswing/followthrough choppy, bunty strokes)
in general i think folks initially refer to pusher as someone with
a) short choppy strokes
b) no pace no spin balls that require
at 4.5+, they stop having short-choppy-strokes, but relative to how hard an opponent might be hitting (or may be used to hitting), the pusher still hits "no pace"... so the sobriquet sticks