How exactly does "the usual bootstrap" work?

[e-pet]

The documentation of the resampling method "boot" of trainControl only states that it does "the usual bootstrap". What exactly is that? Every publication I can find seems to define something different as "the usual bootstrap". For instance, the rms package cites eq. (2.10) in this paper (Efron, 1983) for "ordinary bootstrapping" (which they call "boot") - which seems to be an optimism corrected bootstrapping method? Other versions of "standard bootstrapping" I've seen include bootstrapping without any optimism correction, validating a) on the whole dataset, or b) on the out-of-bag samples.

I tried to find the answer to my question in the code (it should be in workflows.R), but I'm having a hard time following what's going on to be honest.

[crossxwill]

https://www.tmwr.org/resampling.html#bootstrap