Can someone let me know what is the 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.
As Bootstrap came from the 2 famous guys at Twitter, hence sometimes it's called Twitter Bootstrap. Bootstrap 3 is the latest version.(I guess version 4 is on its way).
An excerpt from Wikipedia:
Bootstrap, originally named Twitter Blueprint, was developed by Mark Otto and Jacob Thornton at Twitter as a framework to encourage consistency across internal tools. Before Bootstrap, various libraries were used for interface development, which led to inconsistencies and a high maintenance burden.
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.)
Bootstrap that you have tagged has a description A bootstrap is a series of procedures run when an application starts up or a request over the web is received.