They do NOT collect clandestine intelligence or have anything to do with the military.
The FBI is a national and federally empowered police force - to investigate crime.
It gets a little more complicated in that MI6 has its own "counter-intelligence" section.
"MI5/MI6" were the original designations when both organisations came under the War Office, now the MOD - "MI" stands for military intelligence.
MI5 is the British security service while MI6 is the British foreign intelligence service.
Crudely, MI6 are "our" spies while MI5 is there to catch "their" spies.