If you're using some API, it's probably best to look at the API docs.

If I had to guess, I'd say that top_k is about the beam width in beam search. And top_p is dynamically adjusting the beam width to cover the amount of the probability distribution you specify.

top_k=1 is probably what we'd call a greedy search. It's going left to right and picking the most probable token. The sequence of tokens selected in this way might not be the most probable sequence though.

Again, check the API docs to be sure.

All that said, these are just settings for discovering the most probable sequence in a computationally efficient way. It's still deterministic and still attempting to find the most probable sequence. What I was describing in the previous response was adding some randomness so that it's not deterministic.