BPSK
hi zeerum
what we do in simulation a bit differ from what we should actually do in practice. all passband representation of signals have an equivalent baseband representation. if we have prefect synchronization in receiver both of these representation go to the same point. it's common in simulation when we want to explore phenomena like channel response, pulse shaping, ... but not prefect synchronization, (for simplicity) we can simulate it in baseband.
if you refer to Matlab (esp. 7.xx) all digital modulation perform in baseband and then if it's necessary in your simulation you can upconvert it to your interested frequency.
about your second question I gonna go a little in deep. modulation have two important types, Linear and Nonlinear. Linear modulation in baseband representation are simply a mapping (refer to Matlab). as the input give it symbol index and take modulate sample. but about the difference with analog modulation i should emphasis that in digital modulation we have two critical subsystem match filter, and hard decision. it's because of two different point of view, fidelity in analog communication and accuracy in digital modulation.
hope this help you.
regards.