Is the _error_ in the context of ML always just the difference of predictions and targets?

Question

Simple definitional question: In the context of machine learning, is the error of a model always the difference of predictions $f(x) = \hat{y}$ and targets $y$? Or are there also other definitions of error?

I looked into other posts on this, but they are not sufficiently clear. See my comment to the answer in this post:

What's the difference between Error, Risk and Loss?