innovating: (v) Make changes in something established, esp. by introducing new methods, ideas, or products.
inventing: (v) Create or design (something that has not existed before); be the originator of.
Apple is probably the most innovative company, in that they take existing technology and continually refine it into product. Which is crucial because nobody wants their phone to be a lab prototype.
On the other end, most invention happens in academia. You need a lot of flexibility and low expectations of commercialization in order to really try dramatically new things.
The magic companies of the last century are the ones who could do both, allowing people to have side projects that don't immediately show commercial promise. Bell Labs was a lot like this. So was PARC. And Google to some degree.
I think a lot of Silicon Valley startups now have the worst of both worlds. They feel pressure to monetize and sell for millions, so their creativity is limited and they just barely innovate. They're not content to play, or work on something just because they like it and find it interesting. We hold up Elon Musk as a great entrepreneur, but he started building rockets because he wanted them to exist, not because he wanted to make money. [1]
It takes a different sort of thinking to come up with SpaceX than it does to build Exec or Instacart. A different level of grit and disregard for fortune. It's unfortunately rare to find that spirit matched with incredible focus and ability to execute and sell. And even more unlikely that it gets funded. (There's a reason Elon started both Tesla and SpaceX with his own cash.)
I'm certainly not saying that one should disregard the economics of running a company. But you don't make radical changes in the world when your ideas start from them. [2]
Incidentally, I've actually looked into building ramjet aircraft. (Or scramjet, because why wouldn't you go supersonic?) It's physically possible, [3] but requires a breakthrough in energy storage and composites on the order of the transistor.
I've always thought there are two places in the world with huge market failures: developing world healthcare, and future-tech. In many ways, philanthropy such as the Gates Foundation helps mitigate the first, but I've yet to see anything other than war with a technologically-equal enemy push forward the second. Google is showing some promise which is exciting, but we probably shouldn't have all of our future hopes wrapped up in a single giant online advertising company.
I think we should create a West Coast "Institue for Advanced Study" in the middle of the desert with a few million dollars and a bunch of dreamers who want to get their hands dirty and try ideas that everyone else thinks are crazy. People do amazing things when nobody is looking over their shoulder.
[1] In fact, it seems he had to negotiate like hell to wrap a business model around that company, and got incredibly lucky that Shuttle was retired. You could also argue that SpaceX is still innovation but I would argue that the dramatic cost savings and reusability make it count as invention.
[2] Maybe unless you're a brilliant economist or politician, but how that world works is a mystery to me.
[3] Check out the WaveRider project. http://en.wikipedia.org/wiki/WaveRider