I use Athletics and Acrobatics for very distinct things, personally.
Athletics is training in physical exertion. I call for Athletics checks when a character is either doing something which requires gross physical effort or when someone is trying to exert themselves to surpass the normal limits of what can be done.
Acrobatics is training in physical finesse. I call for Acrobatics checks when a character is doing something with their whole body that requires precision.
As a rule of thumb, an athletics check is all about the body in isolation. Whether you can lift yourself by the fingers of your left hand alone, for instance. It doesn't matter what you're gripping on to, so long as it can hold your weight.
Acrobatics checks are all about the body in the context of the world. Whether you can swing from this bar and land on that ledge is a unique situation that depends upon the exact placement of the ledge and the bar.
An example:
Tim is a High Elf Rogue, trained in both Athletics and Acrobatics. Tim is being chased through a city at night by a dozen cultists who know that the way to a man's heart is through his stomach.
Tim is running across a rooftop and comes to the edge. There's a 10' gap to the next building. Jumping it is purely a matter of whether he can make the distance or not - a Strength[Athletics] check, which he makes easily.
The new building is straight and very long, and Tim realizes he has a chance to get a bit of a lead on the cultists. He attempts to run faster than he would normally be able to, a difficult Dexterity[Athletics] check. He's lucky and makes it, beginning to pull ahead of the cultists. He tries to keep this up for the next round, but fails the necessary Constitution[Athletics] check (Straying away into houseruling, I'd happily allow a player to automatically succeed on a check like this... in return for taking a rank of Exhaustion until the end of the next short rest).
Unfortunately his luck has run out a bit - he reaches the end of the building and there is no next one, only a 60' drop. There is, however, a flagpole 5' away from the roof. Tim tries to jump and grab onto it. This jump requires aiming more than exertion, so he makes Dexterity[Acrobatics] check and passes by a good margin. Once on the pole, he starts to climb down (Strength[Athletics]). Half-way down the pole, he sees a group of cultists have arrived on the street below at a run and are loading crossbows. He looks around and sees a boarded-up window on the building. He attempts to swing around the pole and crash through the window board (a Strength[Acrobatics] check, since it's a matter of the precise application of force). He just fails though, knocking the board away but having to make a Dexterity saving throw to grab the window ledge. Failing that, he falls 15' down the wall of the building before managing a Strength saving throw to catch on to the back of an advertising board on the side of the building. Thinking quickly, he uses his Minor Illusion cantrip to make the sound of a crunch on the ground below, followed by running footsteps. Most of the cultists fall for it, running down the street away in the direction of the "footsteps". The last cultist, though, seems to be suspicious, poking around on the ground and examining the building. Tim flattens himself against the advertising board and makes a Dexterity[Stealth] check to hide there, passing very well. However, the cultist continues to investigate the area, looking at the advertising board as if suspicious.
Holding himself completely still is taking its toll on Tim; he makes a Constitution[Acrobatics] check to hold himself absolutely motionless. Luckily he makes it, and after another glance around the area the final cultist leaves.
Tim waits a short while, then drops to the ground as quietly as he can and sneaks away into the shadows (Dexterity[Stealth]) to make his way to the inn his friends are staying at.
Of course, the whole issue here is a playstyle question, so there's no wrong answer. If it makes sense in your game to merge Athletics and Acrobatics, then you definitely should do it. I'm just trying to illustrate that the 5e default has useful mechanical separation. I'd also say it's a lot easier to merge two skills than to split out a single one, because it's easier to see that two concepts are related than to see exactly the right place to split a single overarching concept.
