Pen testing tells you how an opponent could get into your environment. It emphasizes the potential damage of not hardening the environment by showing how different vulnerabilities might be exploited or identifying insecure IT practices.
Threat hunting tells you who is already in your environment and what they're up to. It deals with the actual state of the environment and shows what threats are targeting the company.
They're both methods used by defenders to bolster their security, but the former deals with possibly scenarios which may lead to a breach, while the latter works backwards- first looking for a breach, then working backwards to a vulnerability.