The difference is that pickling cukes generally have a very thin skin and small tender seeds, whereas regular cukes are larger and have thicker skin and large tough seeds. The thicker skin and seeds make the pickles tougher but they're still better than no pickles at all :)
Some cucumbers are bred to be used for pickles and some regular cukes are just picked when they're small and immature, and they pickle just as well. One problem with buying them in the store is they're frequently coated with a greasy wax to make them look fresh longer (it also seals in the pesticides.) You don't want to eat that stuff and it would keep the brine from penetrating the skin too unless you slice them.
You should try growing a couple of cucumber plants, they're very easy and you can grow them up any piece of fencing you already have or just let them sprawl on the ground. Then you don't have to worry about what they've been sprayed with.