The reason you want to go with fingerprint cards sent to you by the organization that is processing your paperwork is because.....
I live in Florida. When I applied for my concealed weapons permit, the fingerprint card specifically states the agency it is for. If you are getting fingerprinted at the police department and theres a massive ink spill/murphys law, very frequently will the fingerprint tech just grab a new fingerprint card.
That creates a problem because instead of the fingerprint card saying FDLE or FBI it now says "COUNTY JAIL" and it will foul up your paperwork.
As a sidenote: When I went to get my prints done I brought TWO sets of fingerprint cards just in case something happened. Didn't need them but theres your reason.