No, there is no requirement for you to stay at a Disney Resort to go to any Disney park. You do get additional benefits for staying on property, so there’s a lot to consider in your factoring of things.
There are a total of 4 different theme parks, 2 water parks. The theme parks include, Magic Kingdom, EPCOT, Hollywood Studios, and Animal Kingdom. The water parks include, Blizzard Beach and Typhoon Lagoon.