My understanding of background check is to check with the states you lived in the past 5 years and see if you have any bad records or not. What you mentioned should be reference check.

as far as I know, companies either conduct background checks through a third party or by themselves. The contents include

credit score/history

criminal history

drug test

employment history (start/end date; salary if possible)

ethics history (they might call your friends...god knows how they get their info.)

If you claim that you belong to a professional society, etc., they will check record

academic history

etc.

they might check every single word you say. So never lie and take the chance.