Amusement is the action and state of being amused, or interested in something fun/funny. Theme parks where there are rides and roller coasters in the united states are called "Amusement Parks" as well. Entertainment is a form of leisure. Going to the cinema, the arts, theater, and dance for example. Being entertained, would be your emotional state. Recreation is the activity you perform for relaxing. Usually after school or work. In the United States, parks that have sport facilities or trails for hiking are called "Recreation Park".

Entertainment usually refers to music, television, movies, plays, etc. Amusement usually refers to "amusement parks" or circus, with rides and games. Recreation usually refers to outdoor activities like hiking, backpacking, mountain climbing, camping, bicycle riding etc.