What is difference between Bootstrap, Twitter Bootstrap, and Bootstrap 3?

There's no difference. Twitter Bootstrap was the official name for version 1.0 (Twitter Bootstrap). Later the name has been shortened.

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.)