Without exaggeration, does P = NP means P (runs in polynomial time i.e. 1 second on a deterministic Turing machine) must be equivalent to NP (runs in polynomial time i.e. 1 second on a non-deterministic Turing machine)? For example:

P: Get a subset that sum to 0 in polynomial time let say 1 second on a computer i.e. (deterministic Turing machine e.g. the usual traditional computers that has only one possible action that the computer might take and sequential)

NP: Get a subset that sum to 0 on a “specified” computer i.e. (non-deterministic Turing machine e.g. super computers with multi threading processor and large memory that can spawn different threads that generate every possible solution and check them all at the same time. Such that each individual verification thread can run in polynomial time i.e. let say 1 second, and they’re all being run at the same time.