Is there a difference between federal or government intelligence ?

Not necessarily. Government can work at the Federal, State and municipal levels (among others). So Federal intelligence may be more specific than government;

In either case, it might be an oxymoron.
Joke
See @iamthemob

Our governments are at three levels, Federal, State and Local. All three levels have the power to raise taxes and institute new laws. To answer your questions, they are essentially the same, just different levels.

They are both oxymorons: “Federal-intelligence” and “Government-intelligence.”

DAaaaMmmNnn YOU @josie (...in John Stewart’s Voice), you beat me to it. And no it’s not a joke.
Guess, now i have to lurve you.

maybe if you provided some context?