In the context of CSS frameworks, Bootstrap and Twitter Bootstrap are the same thing.
Bootstrap 3 is the third major version of Twitter Bootstrap. (When this question was asked, it had not been released yet.)
(There’s another unrelated definition: to bootstrap a computer program or system can refer to running certain phases of early startup. It’s often abbreviated as “booting”, as in “booting up a computer”. Wikipedia has an extensive definition and etymology which I won’t reproduce here.)