in swing, traditional swing where the ball deviates into the batsman. The shiny side of the ball will be away from the batsman. For reverse swing, the ball will swing back in late when the shiny side is towards him. Hence, reverse.
Cutter is deviation off the pitch. They flick it out of the fingers and wrist in a way that they can get it to move after pitching one way or the other.
So traditional swing can be inswing or outswing. I thought it swung towards the shiny side but I was wrong. When it swings towards the other side of the ball (the shiny side), that's reverse swing, which can also swing into (inswing - off to leg) or away from (outswing or away swing - leg to off) the batsman. Interestingly swing from leg to off is always outswing, even when it knocks over the stumps!...
As for deviation off the pitch, when the ball deviates off the seam (ie. lands on one side of the seam and thus deviates in that direction), that's called seaming. That can also go either way ('seaming in', 'seaming away/out'). A cutter is when the pace bowler puts sidespin on the ball like a spinner, to make it deviate off the pitch that way. Legcutters deviate from (the bowler's) right to left; offcutters from left to right. Whether the bowler or batsman is left- or right-handed makes no difference.
An 'in-cutter', IF such a thing existed (it doesn't), sounds like it would be the same as an off-cutter to a right-hander (or a leg-cutter to a left-hander).
EDIT: On Jan 7, 2011 at 9.23pm AEDT I edited the above to make the following changes:
Traditional swing is away from the shiny side of the ball - Cricketman was correct.
A legcutter always deviates from the bowler's right to left, and an offcutter from left to right, regardless of which hand it is delivered with, or whether the batsman is left- or right-handed.