Here is a really good article about the topic. The gist is that typically in mountaineering, there’s not often an official definition of the “start point”, but the “end point” is back at the start, so people who die midway on the return journey don’t “count”. The “top” should be easy to define, but often, the top of a mountain is a large area, and you aren’t going to hike around looking for which part is just barely the highest. Also, some true summits are habitually avoided as sacred places to the locals.