What are the differences between Athletics and Acrobatics (aside from the stats they are based on) and is there anything interchangeable?
When should one be used over the other?
When I see these two skills it sounds to me like everything that is an acrobatics check could also be an athletics check and I can't think of many situations that apply more specifically to one or the other.
Acrobatics and Athletics are quite different.
Athletics is used for things that are strength based in nature. The big ones are jumping, swimming and climbing.
Acrobatics is used for things that require agility and balance (Dexterity based things). The big ones are balancing, negating falling damage and tumbling.
The thing that they have in common is that they can both be used to escape from a grab. (Acrobatics to escape, strength to break your restraints)
The actions enabled by the two skills illustrate their differences:
These actions all exemplify using force and power (ie, strength) to overcome some obstacle, hence Athletics uses your Strength ability.
These actions all exemplify using your agility and grace (ie, dexterity) to overcome some obstacle, hence Acrobatics uses your Dexterity ability.
Probably the best place to start is to check the handbook (something that I forget to do all the time). The DnD 4e Player's Handbook actually gives a decent description and several examples of the common actions of each skill.
But abstractly, you can't really set aside the ability scores that the skills are based on. What the skill is and how it's performed is informed by the ability score. Personally, when I'm trying to decide which would cover an action I think this: does this action require muscle, or precision?
Strength is all about muscle, and athletic people are going to be strong from their exercise. To jump really high an athletic person needs large leg muscles, to break ropes tying her down an athletic person needs large arm muscles. But neither of them are exactly delicate maneuvers.
Dexterity is about agility and practice, and acrobatic people are going to be precise. To slide through an enemy's legs without getting hurt requires precision, as does walking a tightrope. But you don't really have to be strong to do either.
Some things honestly require both: Someone trying to jump to a really high window AND through it without touching the broken glass on the sides should probably roll both, and failure consequences probably depend on which roll was failed.
I think the confusion comes from real life examples; most people that we think of as acrobatic (gymnasts, martial artists, and uh, acrobats) are also athletic because they do things like jumping, climbing and running, but that doesn't mean that the athletic actions are also acrobatic.
Really the only difference is the default ability associated with each skill. The Acrobatics examples in the Player's Handbook could easily be thought of as Athletics (Dexterity). Splitting it into two skills serves to disambiguate which ability score is more likely to be required for a task, in a similar way as the split between Investigation (Intelligence) and Perception (Wisdom). It also has the effect of requiring separate proficiencies, since the training required for Strength- and Dexterity-oriented athletics is somewhat different (despite having overlap in the real world).
