>(A) (for bootstrapping) The underlying population distribution is
> precisely the same as the observed sample distribution.
>(B) (to get a CI) The underlying population distribution is not
> necessarily the same as the observed sample distribution.
But, there are many more kinds of bootstrap
Non-parametric - treat the sample as if it were the population
Semi-parametric - treat some aspects of the sample as if ...
Parametric a: Discretize a parametric distribution so it can be boot strapped
b: Draw random samples from a parametric distribution (simmulate)
For quite thorough but not too technical account of these issues
Efron & Tibshirani, An Introduction to the Bootstrap, Chapman & Hall 1993