Can you please explain the difference?
QA means you make sure that products aren't duds, you do that by finding what causes the failed products to be made and fixing it.
Meta: The focus on QC instead of QA brings to mind the UK government approach to education, adding more tests instead of using the time/resources devoted to tests to educate the children.
QA addresses your process, from repeatability (e.g. ISO9000 in the cases where it makes sense -- less often than it is used, but sometimes it's crucial), incoming materials inspection, choosing processes that error in directions you want (should you mill material away from a billet, potentially taking not enough, or cast and potentially have the part shrink? Some systems can handle a too-small part better than a too-big one; other systems are the opposite) etc.
QC can be thought of output validation (i.e. testing, which is a lot of it): are my products of the necessary quality/within spec etc? Sometimes you can do 100% inspection, sometimes you have to use statistical methods (there are whole ISO specs devoted to nothing but sampling algorithms).
If you are not clear in your mind about the differences, the jargon can confuse you more (e.g. incoming materials inspection is sometimes referred to as "incoming QC"). But from this you can see why you "can't test your way into quality": the tests happen too late in the process.
QC is looking for bugs for in the usual suspects for every output and fixing them as you discover. This can be automated and/or manual.
QC is making sure that your output is good before it gets to QA.
I have to emphasize the sentence you ended your comment with. Anybody who has worked in volume production has heard this phrase too many times to count.
People who never learned the difference between QC and QA never seem to understand this phrase either. Doesn't mean they are dumb, but does mean they don't even understand the scope of what they don't know.
Another common misunderstanding is the dynamics of the learning curve. Costs of high volume production drop precipitously (and quality typically increases proportionally as well) but incrementally as volume goes up. A common misunderstanding is that that means you work incrementally to get better. But that is true for systems set up from the start as high volume systems. Tesla the company has been at it for almost 15 years (Musk has been there for 13 of them) and still appears to be in low volume manufacturing mode.
It's not super surprising when you consider that Space X makes small volume, bespoke hardware. A big backend system is still a one-off even if you run huge volume through it. Cars, phones, etc are a completely different game.