I know that's probably a naive answer, I honestly don't even know how a hash table works. I know how a hash map works, at least some implementations use a linked list as a bucket. So the hash gives you the bucket, then you linear search the bucket for the element. Buckets should be small so the time to search them is negligible, giving O(1) lookup and insert performance.
Obviously this is different from what's being discussed here, this data structure doesn't even really get "full" but it's also the only implementation I know is in practical use. Not sure why one might use a hash table instead