E.g. you'd use JetKVM-like devices to re-install your OS via emulated drives, remotely control power (including hard reset, not just WoL and software shutdown), change BIOS settings, or troubleshoot a crashing box - all without relying on any specific software/capabilities/behavior of the given box. Meanwhile you'd use remote desktop software when you just want the desktop to present itself remotely.
I do VoIP phone systems for a living and this is why I deploy Supermicro mini-ITX servers, so even if something goes totally sideways as long as the client's IT is competent enough to get me remoted in to their voice network in some way I can troubleshoot it fully and in many cases fix it without leaving my desk possibly half way across the country. If it's an actual hardware problem and I can't fix it remotely I still then know for sure what's wrong and whoever's going on site can be properly equipped for the actual problem rather than having to bring everything.