It's absolutely possible to make black holes in general relativity without having any matter because gravitational waves and similar kinds of distortions of space time can effectively have energy. In the real world, we can imagine that we can create a completely by gravity, but we don't think it's going to be the most common thing. Having said all that, if it did happen, you have zero way of knowing that they're the same outside. That's the consequence of the No Hair Theorems. Black holes look the same given a certain amount of mass, spin and charge. It doesn't matter what they're made out of. There's no difference between a black hole that was created by gravitational waves