Revolutionary Card technique goes into great detail on the cop and the palm. Marlo covers a bunch of versions. A cop can have more angle sensitivity, but the hand is generally more relaxed. A palm is more secure but the fingers are more confined (generally).
An action palm uses another action (fanning, shuffling) to obtain a palm. They are great because they provide the magician with built in misdirection. The way that the card is held in the hand may be unique to the action palm, or it can be more of a classical "palm". The same can be said about cops.
Marlo goes through some classical cops and palms as well as some funky variations. If they feel or look weird while you are reading, check them out in the mirror and try to turn your hand till it hides the cards a little better. Cops and palms can have funky angles. It's best to experiment to fine out how they are best viewed.
Both are moves that make many magicians blush