Often these two terms are used interchangeably, as synonyms, but that are not.
Creativity is a part of the process of innovation, an integral and key part, but nevertheless, just a part. It is, as Sir Ken Robinson so memorably said in his great TED talk, “Creativity is the process of having original ideas that have value” .
By contrast, innovation is to my mind the process of taking the output of the creative process and putting in place the steps to extract and leverage the implicit value of the creativity, making it explicit. Thomas Edison, perhaps the most celebrated inventor of all time, certainly the individual with more patents to his name than anyone else, before or since, famously said “Genius is 1% inspiration, 99% perspiration” recognising the distinction between the creative spark, and the hard work necessary to turn the idea into a product, service, or process.
For enterprises to flourish in today’s competitive world, they need to encourage a culture of creativity, again as stated by Sir Ken in the TED presentation “If you are not prepared to be wrong, you will never come up with anything original” and back that creativity with a management culture that gives the creativity life.