It is a general term that describes many different species of parrots. It's a descriptive rather than a taxonomic term. A parakeet is a small to medium-sized parrot with a long tail. The common house pet that we usually refer to as a parakeet is merely one example of a parakeet. Its real name is the Budgerigar, or Budgie.
Parakeets are parrots.
So are macaws, cockatiels, amazons, cockatoos, and so on. You could say that parakeets are to parrots as sports cars are to cars. Although some ornithologists do call them conures, most call them parakeets. Conures are South American parakeets. Later, as knowledge of these birds grew, that single genus was broken down into six or seven different genera.