It is different than mining gold in that very important way. However gold has a difficulty adjustment of sorts, for example during the California gold rush it was initially very easy to find gold in streams by panning, but this changed once the area was overrun with hopeful prospectors. Bitcoin is superior to gold in many ways, one of which is a more effective difficulty adjustment mechanism. I agree that bitcoin is not "discovered" in the same sense as gold or other mining, definitely not a perfect analogy. But I think the mining analogy is still useful because it gives us an opportunity to highlight this crucial distinction. Plus it's so firmly fixed in the public consciousness there's no way we're changing it now.

Also, one thing Bitcoin mining does discover in a sense is the cheapest sources of energy.