Fleet Ops was an element of the Galactic Republic's military during the Clone Wars. Along with the Logistics battalions attached to the Grand Army of the Republic, it was responsible for the deployment of personnel and supplies to front-line units, under the central authority of the logistics center at Coruscant Command HQ.
The name of Fleet Ops implies that it was specifically concerned with spacegoing fleet units, although it is not clear whether it was a preexisting element of the the Republic Navy, or a new organization established to deal specifically with the assault ships and other capital ships serving directly with the GAR.
Fleet Support was a branch of Fleet Ops dealing in refits, repairs and general maintenance of all GAR spacegoing vessels during the Clone Wars. It was also responsible for maintaining various Fleet installations and ordnance depots, like Ord Mantell and Coruscant Fleet Support Depot, throughout the galaxy.