Are parakeets the same as budgies?

OK so i kinda of want a bird in the parrot family.i wanted a parrot/macaw but they have rather large claws and beaks so they seem a bit more dangerous to me.instead i want a budgie or a parakeet,but are they the same thing?my mom said budgies are more tamed.plus they are a bit longer and have a flatter face.other than they they aren't really that different.are they the same thing?