I think creativity is indeed thinking up new concepts/things. Innovation is making this new concept/thing practical in a novel way. Creativity is dreaming up a new invention and innovation is making it real in ones own unique way. When you bring something new into existence you can say you created it. You cannot say you innovated it. And again when you improve something that already exists you cannot say you created it but you can say you innovated it.
Henry Ford created the assembly line for car production. The Japanese perfected this concept by introducing their own unique innovations/changes/improvements. Lots of people are creative but they are not innovate enough to make their creations practical. Innovation makes creativity practical and efficient. Most inventors fail because they are not innovative enough. Most painters are creative but when they introduce innovation in their creation/art they become artists. Without creativity there is no product/concept that needs implementation and once something new is thought up it needs innovation. Research and development is about innovation. Sometimes innovation can lead to a realization of the creation being impractical and so this new creative idea may be abandoned and a new creative idea may be born thus innovation may lead to creativity. Innovation is giving a new direction to an existing idea.
There is confusion and fuzziness between creativity and innovation because indeed innovation is about creating new ways to implement the existing/created concept. Thus they both have creativity in them. Innovation also involves elements of creativity.
All PhD courses are for researching innovative ways of doing the old stuff in better and more efficient ways. Innovation is about solving existing problems. At a deeper level innovation is research. At the research institutes they are creating better and better innovations for existing solutions. One does not require a PhD for creativity but for innovation at the cutting edge highest level a PhD is almost an essential requirement. In fact at the university level innovation is preferred over creativity. For any newly created ideas are doubted till they can be scientifically defined, measured and tested and this involves complex and time consuming investigations not to mention finances. However anything that is already in use and has proved its utility then any improvement through innovation is accepted whole heartedly. My own invention, ‘Vacuum power generators’ is based on a sound principle that, ‘nature abhors a vacuum’; however it was rejected at the highest levels of the US government because of another sound principle ‘The law of conservation of energy’. The law of conservation of energy says that the energy you put in will give back less due to friction. But in nature there are exceptions to this law! Hydrolic pressure, fulcrum power all give back more energy then they take in. And vacuum power is the fulcrum of wind power. But it is an unproven and too radical an idea and also requires tons of money to make a proto type. On the other hand my little innovation of tweaking a little improvement in the baby milk bottle I was able to sell right away.
Creativity is essential for innovation for a product must exist at least in a concept stage for you cannot innovate anything that does not exist. Thus innovation depends on creativity while creativity does not depend on innovation. Though the better success of creativity depends on innovation.