"I am on it" vs. "I am at it"

What are the differences between I am on it and I am at it? What does the latter mean? I found the definition of the former on Urban Dictionary and understand that it means I'm going to solve it shortly. For instance:

A: This guy is making noise and I cannot concentrate on my work.
B: Don't worry, I am on it.

I've also heard:

Oh, those reds are at it again.

in the context of a feud between reds and blues. Googling did not help.

If I say "I am on it", then "it" is a problem that needs solving, or a task that needs doing — but it's something finite. I'll be finished doing it, sooner or later.

If I say "I am at it", then I'm doing some job, but there might not be an end in sight. It could be something like "doing housework", or "earning money", that isn't ever going to be finished.

I am on it in your first example sounds like a shortened version of I’m on the case, a colloquial way of saying that the speaker is dealing with it. In the context of some kind of dispute, as in your second example, they’re at it again means that they have started doing again whatever it was that was a component in the dispute.

According to OED if you are at it, it means that you are engaged in some activity, typically a reprehensible one:

oh dear, they are at it again.

On it on the other hand means that you are about to start working on a specific task or problem; or you are already doing it and it's under control.

Operator: Officer, we have just got a call that there is a burglary going on in your area. Officer: I am on it.