For me it's not the same notion. Imho a proof is by "abstract nonsense" when it is a relatively short sequence of seemingly uninteresting steps that end up proving something non-trivial in the end. And you're left wondering how this stupid symbolic manipulations which looked just like a sequence of reformulations of the initial thing could have possibly proved the statement. This appears a lot in category theory because the manipulated objects are very rich and usually there are a lot of different ways to describe the same thing. Hence you can sometimes just dive into such abstract tunnels and end up at a quite different location giving other insights.

Boilerplate in proofs is usually what we call "administrative arguments".