The Built-In tab of Blocks Editor always has pretty much the same blocks available. The "pretty much" caveat is there because each update (which you get automatically from the Google Labs developer heroes) adds new blocks from time to time.
Note
Frequent the forums at http://appinventor.googlelabs.com/forum to keep up with all the new goodies.
The My Blocks tab is a totally different animal. The number of drawers on it depends on what components you've dropped in place in Design.
For every component you add in Design, a drawer for it is automatically created in Blocks Editor. We'll be looking at and using these drawers during all the many examples to come.
Now, a short quiz, and you may go out and play with blocks.