You should be more specific. All these three could be the 
same if this is just for a Login page. The environment may 
change for each testing. 

I am surprised someone asked you this question in an 
interview.

Smoke Test - just to verify the page or not

Functionality Test - validating the Login page for its 
contents such as User name and password text fields 
followed by 'Login'/ Submit button. We need to enter the 
valid and invalid data and try to enter the submit button 
and verify the behaviour of the page.

Regression Testing: After defects fixes or any change 
requirements added to login page/application. Retesting the 
same defects for the impact on the application / login page.