游 is verb. 游泳 can be verb or noun. 鸭子在水里游泳。 The duck is swimming in the water. 游泳 here is used as a verb. 我参加游泳比赛了。 I have joined a swimming competition. 游泳 here is used as a noun, a kind of sports.

As a Native Chinese, 游and 游泳 are big differences. 游 it can combines words as 游泳。游水。someone or something move in the water. 游资move capital。游走walk。游牧nomad。游行march。游学study tour.上游。中游。下游。one part of river.交游。commute travel,旅游 travel. etc 游泳 is word formation. only means swimming. so you see the 游and 游泳's difference? single 游 basic meaning : something move in the water or journey. So I probably imagine 游水 swimming or 旅游travel. but it is not say I am swimming,我在游。 it like a fragment it is not complete word. 我在游什么呢？it needs complete thought on it.march or study tour. 你游过来吧。please you swim over here. then it means swim. 我来中国游一个月。I trip to china for one month. Is it clear you can understand?

游 це скорочення від 游泳