When a jump point is stabilised any ship can do standard transfer, which allows you to design ships without jump drives.
Standard transfer dumps the ships always at the centre of the jump point on the other side.
Squadron transfer will dump the ships in a random place within X radius of the JP, Squadron transfer can't be done without a jump drive, but you only need to use squadron transfer if the JP is guarded on the other side.
afaik, there is no difference in how squadron transfer works on stabilised and not stabilised JP.