The meanings of the two words often overlap. For example, if you say "The audience clapped at the end of the performance" or "The audience applauded at the end of the performance", the meaning is the same.
They are not always synonyms, however.
"Applaud" means to express appreciation. For example, you could say "I applaud your courage", as a more formal way of saying "I think you're brave".
"Clap" is simply the movement of bringing your hands together to make a noise. This doesn't have to have anything to do with applauding. For example, you might clap your hands together to scare away a bird or a cat. Groups of people sometimes clap slowly to show disapproval of someone or something, which is the exact opposite of applause.
They aren't exactly the same. Clap and applaud can be used interchangeably when referring to a positive response to an event or performance. Clap also has a number of other senses meaning "to strike together" or a sharp, loud noise. For example, I heard a loud thunderclap in the distance. You can clap a few times to gain someone's attention or turn a light on or off. However, using applaud in the same case wouldn't make any sense at all.
https://www.merriam-webster.com/dictionary/clap
