It goes wherever you want to put it! But really there's a million ways to do eyeliner. Putting eyeliner on the "edge" (aka waterline) that you're describing is called tightlining, and it's pretty commonly done with more dramatic eye looks. Most people that use liquid eyeliner put it on/above their upper lid lashes and extend it out. You're right about going all the way around the eye - it's not a super flattering look on many eye shapes, and it's a little bit out of style right now. My favorite thing to do with non-liquid eyeliner is putting it underneath the outer third of my bottom eyelashes. I usually do my eyeliner either as a classic wing, or like the day look in this blog post: https://www.julep.com/blog/day-night-looks-with-sweep-neutral/