proof of work is similar to brute force, but PoW is used to…

proof of work is similar to brute force, but
PoW is used to generate hashes for bitcoin blocks with a certain number of leading zeroes, which entails probability and assumed energy expenditure
proof of work can be used in other ways as well - eg: for message verification or other types of computation
https://en.wikipedia.org/wiki/Proof_of_work#List_of_proof-of-work_functions