To hit a/the wall

Sometimes you hear someone say, or you read, "then he hit a wall" --- meaning what exactly?

Runners "hit a wall." It's a point where the runner is exhausted and in pain. But if she keeps running, the runner can go past this point. "Get a second wind."

Am I right sports fans? I have never experienced this. I've never run anywhere in my life and don't plan to.

Your phrase is also used to indicate a dead end or obstruction as in "The detectives looked at all the leads in the case and then they hit a wall".

Well, aren't these two different things? A wall you can get beyond if you try, and one you cannot? Which does the phrase usually mean?