Ok I have been arrested like three times, booked, and finger printed for the same charge which is a felony charge its still under investigation have not been to court nor charged for it will that come up on either check

Ok, Fingerprint, merely is a proof of check of ID, a Finger print check will show if you have ever been fingerprinted under any other name and/or confirm you have been fingerprinted under the current name. ** more people are fingerprinted for non criminal acts each year than criminals.
It will also show if that fingerprint is wanted under a warrant if that person has never been fingerprinted before but prints on file as a wanted person.

From the names or name they verify on the fingerprints, they run a NCIC ( government) background check. Some systems, like live scan, do both at the same time.

Other companies you may want to work for, many not use government criminal searches but use private companies,

So we can not tell you if they will show up or not, since we don't know who is doing the background search and which type they are doing.

Also if your job is for police, law enforcement or a national security position, arrests will show up for them.

So could they show up, yes it is possible, will they, no, most likely no they will not.