The difference between Leisure and Recreation is, leisure is more relaxing. I.e. Reading a book, watching television, playing Video Games etc. Whereas recreation is more interesting and active. I.e. swimming, going to the gym, running etc.
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Assuming you're asking for 'the difference between'.. Sport is a form of exercise - usually with a specific purpose. Recreation is any activity (including sport !). that is not paid. For example - reading, cooking, pottery, cycling and playing Board Games - are all recreational activities.
no although it could be if you believe that recreation is an unorganised activity and that sport is an organised activity