Well, technically, parakeet is a term for any small parrot with a long tail, so there are dozens of species that can be called 'parakeet'. But budgies are the most common parakeets by far, so most of the time, if someone just says parakeet, it's safe to assume they mean budgie.
Maybe you are thinking of the 2 breeds of budgies? There are American and English budgies, the English ones tend to be called budgies instead of just parakeets more often, but both breeds are budgies. American budgies are smaller, more active and energetic, and possible a little longer-lived. English budgies are bred for show and are larger, calmer, and have thick feathering on their heads that gives them a very grouchy look. Both can be good pets. The most important thing for taming and bonding is to get a young budgie - look for one where the stripes on the head extend onto the forehead; very young budgies may also have a slightly darker beak. Also in very young budgies, the cere will be pink or purple regardless of gender (though sometimes you can identify females by them having a slightly whitish cast to the cere, especially at the edge of the nostrils).
