If you want to get down to basic functions, you could use water for either. The problem is that each oil or fluid is made to a purpose and has different additives as well as different fluid bases. It's not a good idea to mix different fluids for this reason as the additives may react with each other and destroy seals or bearings. Stick with the manufacturer's spec for the purpose.
ALL of these are a type of "hydraulic oil":
Brake fluid
Power steering fluid
Automatic transmission fluid
Tractor transmission fluid
Motor oil
Jack oil
And there are various grades and specs within each.