The younger brother of Stephen Paddock has a rap sheet of a hardened criminal ... light-years different from the brother who slaughtered dozens of innocent people.

Bruce Paddock currently lives in California, but he's led a nomadic life. TMZ has pulled court docs which show he's been a regular in the criminal justice system. Among his arrests ...

-- Criminal threats

-- Arson

-- Vandalism

-- Petty theft

-- Burglary

-- Weed

-- Driving on a suspended license

-- Contempt 

It's unclear how many of these resulted in convictions. We know for sure the 57-year-old was convicted of petty theft with a prior, and vandalism. Don't confuse Bruce with Eric, the Paddock brother living in Florida, who's been speaking to the media.

BTW ... Paddock's father was a bank robber who was once on the FBI's 10 Most Wanted List.