Yet to use a faceplate on my big lathe or turn between centres myself ! I've not had the need to use either straight or bent dogs because if a job will fit in a chuck I'd much rather use that. In the good old days dogs were much used because chucks were expensive. Less call for dogs now, though they're still useful for some types of work, which might be your thing of course. However, if unsure about straight and bent dogs, maybe they aren't needed at all? Yet! When one is needed, you'll know exactly what to buy!
As Bo'sun explains the bent ones are meant to engage in a hole in the faceplate, which is fine and dandy if the two fit together. (Old lathes had a specially slotted plate for bent drive dogs, but general purpose faceplates are far more common nowadays.) A straight dog might be easier to fit if it has to be driven via a bolt or some other arrangement. Both types of dog might need to be fiddled into position.
Made some different dogs once for the one and only faceplate job I ever did on my mini-lathe. Clamps fouled the job so I had to shape some metal specially to suit. Never needed them again…
Dave