Proof of work - does the equipment matter? It technically doesn’t matter whether I am using a super computer or a laptop to do the proof of work, it’s simply that with a super computer I can go through the attempts much faster, which means I have a higher chance of solving the problem before anyone else and therefore claiming the reward, right?
Right.

The proof of work is computing 2 SHA256 of a sequence of bytes that represent the block header to find a value lower than a target. It doesn't matter if the 2 hashes are computed by an ASIC, a CPU, a GPU or a HP-48. What matters is the number of hashes you can compute per unit of time.

That's why the power of mining hardware is measure in MH/s, GH/s or TH/s (mega, giga and terahashes per second).