This is the last I'll speak on this subject as I feel like I'm just getting more confused the more i think about it, but I'm not so sure I agree with above poster.
I think your initial intuition re: the nature of the distinction is correct. They really are 2 sides of the same coin. Every obligation/promise could in some way be interpreted as a "condition" species. A 2 sentence Contracts MBE hypo of a homeowner selling his house to a buyer with no indication of TIMING can invariably be interpreted not just simply
Promise 1: Hand over warranty deed of House and
Promise 2: Give $100K.
Once again, if there is no indication of Timing. It will be assumed based on the facts that these are conditions concurrent. The logic is that both obligations do not require a ton of time. Both involve the exchange of documents or paper after all.
If, however, one promise takes noticeably longer than the other, this time between a homeowner and a builder,
Promise 1: Build a garage
Promise 2: Give him $10K.
Then the PROMISE that takes longer, "in stages," will be assumed to be the condition precedent, since that goes FIRST, which upon its completion, will trigger the other party's obligation to pay the $10K.
The only reason to distinguish whether "build a garage" is a PROMISE or a CONDITION PRECEDENT depends fully on the issue of the case/hypo/MBE question if timing is an actual concern. These terms are not mutually exclusive... not at all.
I imagine that while every promise is a condition, not every condition is necessarily a promise. For example, if you condition your performance (e.g. sell buyer your Jordans) based on the Knicks winning the NBA Championships (

), that condition doesn't have anything to do with you assuming you don't own the Knicks or poison them. It's an external, independent event of which you have no control. In that situation, the condition is not a promise.
However, every promise is a condition in that every promise has to have some element of TIMING... because we exist in the physical world of time-space. And unless we attach TIMING of obligations to promises, we WILL NOT KNOW who is truly breaching, since both sides could argue whose TURN it is without the conditions telling us the ORDER of promises.
Honestly, don't worry about this lolol. I honestly can't imagine this ever being an issue.
If you see a condition problem on the MBE... well, it's hilariously obvious they want you to focus on Conditions. For fuck's sake, answer choices a, b, c, and d have the words "condition precedent," or "condition subsequent" plastered all over it. Then put your Condition hat on and apply Condition Rules, and get your Condition answer, and you're good to go.
As you can tell from everything I've typed, the truth you're searching for is closer to bullshit philosophy on what "X" means... I mean... what does it REALLY mean as you're stoned out of your mind.
It's not important. It's virtually impossible to miss out on what the exam makers are asking for whether it's a MBE question or a hypo, there can be no confusion.
As you've already stated the end result is the same in that a breach of the K has occurred.
Then to calculate damages, you put on your DAMAGES hat on and proceed. I'm not ultra-knowledgeable but based on my studies, I don't see any reason to differentiate damages based on whether a condition has been broken, or an actual BREACH has occurred, since it basically just boils down to the same thing.