Is being creative also innovative?

I don't think there is that big of a difference between creativity and innovation, I believe that creativity is a part of innovation but is also its own process.  Once an new idea comes about the next step is the creative process, but for it to be innovative this creative process has to be fully subjective from any other designs that can influence it. Creative people sometimes use other peoples' works or forms of art to inspire their creativity. This is where being creative generates its own process and parts from being innovative. 

Artists sometimes may take other works of art and recreate it into their own, which may come out very lovely, but it is not innovative. Being innovative when it comes to art and designs means that the overall idea or concept is something you generated on your own and you may also develop on your own. Innovation is essentially creating you own path, in this case its creating your own work, from scratch. Creativity comes after innovation but it also happens during innovation when developing your idea, but to be innovative this idea has to be new and fresh, not inspired by another design.