Clapping is bringing the hands together to make a sound. Applause is a more general term, which can include clapping, but also whistling, shouting and cheering, and arm or hand waving etc. Applauding is a verb. Applause is a noun Make note there than a single word and the idea associated with it can have both Verb and Noun form.

Applauding is indicating that it is happening in the moment... Applause implies it happened past tense and clapping is a slang type version of applauding.