the difference between the drupal login "block" and mysite/user/login I trying to understand the difference between the default Drupal 7 login block and the login provided at mysite/user/login.

From my own understanding, it would appear that the default login block provided by Drupal 7 only logs you into the web interface and the login provided at mysite/user/login is a page provided for you to login through your website.

I have come to this conclusion because if I log out of the web interface and try to login at user/login, nothing happens (I enter my credentials, but nothing happens).

This is my understanding.

If my understanding is wrong, I would appreciate it if someone could please correct me. If I am correct, could someone please provide a good tutorial that teaches one how to use the login page to validate a user and "transfer" the user to a validated state?

Thank you.
There is no such difference. Both forms provide the same input fields and use the same validation and submit handlers. The one is generated by user_login(), the other is generated by user_login_block().