Consider a dataset consisting of a collection of observations. In most applications, these observations do not represent the set of all possible such observations. Hence we call this collection our “sample,” and we refer to the number of observations as our “sample size.” It may seem counterintuitive, then, that bootstrap sampling, which involves taking samples of this sample, would not be considered a “subsampling” technique.
This is because “subsampling” does NOT refer to taking a sample of a sample. Rather, subsampling refers to taking a sample without replacement. By contrast, sampling (including bootstrap sampling) involves taking a sample with replacement.