You can make as many slight variations as you want by creating a specific instantiation of a hard problem with different constants. But we don't know how many meaningfully different hard problems exist.

These are problems that have been studied for many years, that are more-or-less central to mathematics, and where we have good reason to think that an efficient solution would be extremely surprising.

If you have much lower standards, there's going to be infinely many that I can't personally solve. Or if you have impractically high standards, there could be zero hard problems, if they just so happen to all have efficient solutions that we haven't found yet. We can't formally prove any of these are hard.