My take, is that all tractors now have a hydraulic system. Pump or two to feed power steering and to feed the FEL or auxilary hyd. cylinders through control valves.
In addition, the transmissions come as gear or hydrostatic. If hydrostatic transmission, there will be pedals or lever to operate the direction and speed you will go. If gear, there will be a gear system of some sort.
For both tranny systems, the transmission fluid is the hydraulic fluid, and in one reservoir, and will have one filter most likely, plus maybe a screen to pass transmission hydraulic oil through for cleaning.
The engine will have its' own oil system separate from the tranny/hyd. system.