What is considered biracial, mixed, interracial etc...?

Some friends and I were having a discussion about what it means to be those things. One girl's father is from
Canada and has French, Scottish, Russian, and some other stuff that she said. Her Mother is from the States and her background is Irish. 2 said she was mixed and 3 of us said she wasn't. If everything you're "mixed" with, fits under the Umbrella of Caucasian, Ima just go with you're white, and a few in the discussion agreed. My personal theory has always been, if you can check one box for what your race is, usually you're not mixed.   
Example. Usually the options I see are...
-African American 
-Asian American
-Native American 
I was always told to check other. My dad is African American but has Irish, French, and a bunch of other different races in him, and my mom is Hispanic. My boyfriend is only African American, therefore I would classify our relationship as interracial. 
*forgive me if I get races and ethnicities confused. Correct me if I'm wrong please.