... I thought regression testing is a more general concept, just "find out if we broke something" ...

It is (see Regression testing). (I like the word "just" in that quote.) In the most common notion of regression testing, you attempt to define all critical inputs and their correct outputs, a test set that can grow very large. (Can we call this "absolute" regression testing?)

In the process you describe in the OP, you "just" take some input data set, run it through a process, and whatever the heck the output is, that's the correct output; if the next run has a different output, something broke. (Perhaps we can call this "differential" regression testing.)