Detectives work for police departments and other government agencies and investigate crimes in their assigned geographical regions.
Private investigators work for themselves and investigate whatever people will pay them to investigate... cheating spouses, industrial spying, and other civil type cases are all typical.
Note: People usually hire private investigators based on training and reputation. It can take a very long time to build that if you have no prior investigating experience.
Sometimes there's Justice...
and sometimes, there's Just Us
1*
In memory of DCLaw- EOW@RealPolice 02-20-2007.
We won't rest 'till we find the mutt.