I think innovation is important and difficult to encourage. It is something that, like Peter Senge's learning organization grows, when the right environment is maintained.
I'd steer clear of trying too hard to distinguish between invention and innovation. According to an online dictionary, innovation is, "a new method, idea, product, etc."
What that all has in common is the word "New." New ideas, may be the source of new products or the source of new methods, in either case, the new idea had to be embraced by the team, implemented and worked with, and often improved. Not every work environment provides room for those actions to take place. In fact, if my career is any example, most don't.
Rather than discuss what to do to encourage innovation, I think I'll create a list of things that will kill innovation. Avoid these in your organization if you want innovation to thrive:
1) Failure = consequences
Too often, people are afraid to innovate, because if their idea fails, and any risk is realized they'll be reprimanded, written up, ridiculed, or somehow suffer negative consequences. This sort of culture will kill innovation...it simply isn't worth the personal risk. Your innovators will find better jobs elsewhere, and your rule followers will stay. Your operations may run smoothly, but your organization will be devoid of innovative ideas, methods, and products. You can't afford to belittle or punish failure, failure is the path to innovation and success.
2) "I don't think that will work, because.... NEXT."
Some of the best ideas I've seen, seemed like a really bad idea when I first heard it. This is for a variety of reasons, but the primary reason is that people are horrible listeners, and we don't think we are. We actually think we listen, so when we say no, or poo-poo and idea, we think we are disagreeing with what someone said, rather than some jumbled mess in our own head, which may or may not resemble the actual idea being presented. If you or people on your team think you are listening, think again, and try harder. It isn't possible to explore and improve on an idea without first listening, and considering the benefits of the idea being proposed. Maybe it leads to an alternate idea, maybe it needs some tweaking, but what it always requires is engagement, and people who know that they didn't really listen the first time around.
I love watching soccer. Two of my kids are on soccer teams, and I was glued to the TV for both the men's world cup in 2014 and the women's world cup in 2015. One thing I noticed about winning soccer teams, is that they may be in competition with other teams, but they aren't in competition with each other. Rather, everyone on the team is focused on team success, and what it would take to propel their team to victory. Players always have the highest of praise for their team mates and they often say things like, "I'm so proud to play on a team, which is filled with such incredible people." This allows them to work together, and not be focused on individual glory. In a business environment, this translates into collaboration, acceptance of innovation, and a team effort to improve on innovations. A culture of internal competition and "me first" will kill that off, and make your organization mediocre.