Slip and Move do basically the same thing, they jump to a location within the loop. Slip came first and is more limited in where you can go, but also more controllable. I forget where it came from, it might have been a request, or just something I tossed in one day to see what would happen. There wasn't a lot of thought put into it. I think it worked like this...
There are three variants: Slip, SlipForward, SlipBackward. All three look at the Slip Mode parameter to determine the "unit" to move. The functions each allow an argument that is the number of units. Slip must have an argument, a positive (forward) or negative (backward) integer. SlipForward and SlipBackward accept an argument but if you don't pass one they assume 1 unit. The units in Slip Mode are:
subcycle
cycle
start
relativeSubcycle
relativeCycle
time
If you use units subcycle and cycle, it jumps forward or backward to subcycle/cycle boundaries. So SlipForward means jump to the next subcycle and SlipForward(2) means jump to the subcycle after the next, etc.
If you use relativeSubcycle and relativeCycle it jumps the length of one subcycle/cycle but relative to where you are at the moment. Example: the loop is 1000 samples long and there are 4 subcycles, each subcycle will be 250 samples long.
A relative jump just adds 250 to the current sample location. A non-relative jump will only go to 0, 250, 500, 750.
slipMode=start just jumps to the start and is effectively the same as the new Start function, arguments don't matter.
slipMode=time is the least useful, it treats the argument as a number of milliseconds. So if you found a compelling reason to jump to exactly millisecond 1234 of the loop you could do Slip(1234 slipMode=:time)
Move is actually more of an internal function that is used for several things including Realign. Here the argument is any sample location within the loop, but in order to use it for anything other than Move(0) you would need to be in a script and doing some math.
There is another relatively obscure function that you might find interesting Shuffle. This reorders the loop subcycles according to a few selectable patterns. If I remember right, Reverse means to make subcycles 1 2 3 4 be 4 3 2 1.
Shift would make 1 2 3 4 be 2 3 4 1 and you could apply that several times. Swap I believe worked in pairs so 1 2 3 4 would become 2 1 4 3. Random just moved them randomly.
Finally there once was a way to pass a "shuffle pattern" in as an argument. That was a string of numbers where you could define a pattern like "4 3 5 1 8 2 7 6" and it would scramble it that way. I think someone tried that a year or so ago and it was broken, so it probably still is.
Slip and Shuffle both obey Quantize. I don't think Move does because it is used for internal forced jumps.