Though these terms are used interchangeably, these are actually different.
Play
Play is spontaneous. It is usually a creative activity but has its own limitation and space. One plays voluntarily for fun and pleasure. Play, however, is a broad area which includes both games and sports. The distinctive features of play are that they are free, separate, uncertain, governed by self rules and creative.
Games
Generally the word games and sports are used together. A game is an activity involving more players, defined by a goal that the players tries to reach, and some set rules to play. By masses, games are played primarily for entertainment or enjoyment. The difference of purpose differentiates sport from game, combined with the notion of individual or team skill. Games are also played on the basis of a set of rules. A game is defined as a goal that the players try to achieve. A person who participates in a game is known as a player.
Sport
A sport is a physical activity carried out under an agreed set of rules, for competition or self-enjoyment or a combination of these. Sport are the kind of activities in which similar kind of body movement is repeated over a long time. For example, swimming and running and almost all the track and field events come under sport. Sport involves an activity or activities where the mental capabilities of the sportsperson are judged. In a sport, it is the sportsperson or the individual who determines the outcome. A person participating in a sport is called an athlete or a sportsperson.
