Pressure Relief valves

From a mechanical standpoint, no there is no real difference. From a materials of construction point of view, yes, there can be a difference. Relief valves themselves do not vary much in design, therefore can work in either liquid or gas service.

The material they are made from does vary depending on what kind of service they are put into. An example would be that a hydraulic oil relief valve could be made from carbon steel, but if this were put into service with water, it would rust and not function properly. Elastomeric seat materials as well as the body of the valve should be checked to make sure they are compatible with the service they are being put into.

doesn't the valve design (orifice) itself depend on viscosity? which is almost constant for the gases

Yes, there is a correction called Kv in the API RP521 documents. for reynolds number under 4000, the factor drops which means you need a larger orifice. You may also have rerate the pressure drop and in the inlet and outlet lines of the relief valve.

There needs to be difference because in case of gas pressure relief valve, you need to design the orifice of the relief valve for maximum possible flow of the gas in the system. If the orifice is small, the pressure will not reduce or keep on building up unless sufficient quantity of gas escapes from the system. This is typically true for steam lines, where, any relief valve after a pressure reducing station needs to be designed for full capacity of the pressure reduceing station.

In case of hydraulic system, this may not be critical as the pressure would drop sharply since any liquid(hydraulic oil) used is not compressible like gases.

If you are asking whether or not you can put a gas relief valve in liquid service or vice versa, the answer is probably no and at the very least should be checked with a manufacturer prior to installation. There are a lot of considerations similar to what you mentioned about the orifice size, the sizing equations for liquid are different than for gas.

Take a careful look at your sizing case(s) and compare the two results, I would be surprised if they are the same. Also, take a lot of care sizing and installing these valves, they are really the last line of defense between you and the forces of Nature that you are trying to control.

If I could plug the API standards for a minute, API-520 and API-521 are an excellent source for a good introduction to relief valve calculations and design considerations, at least in my opinion. If you can get your hands on these standards, you won't be disappointed. They can get you to the point that you can have a good discussion with a vendor's engineer.

Gas expands through a pressure relief valve, whereas a liquid does not (not much, anyway). So the sizing will differ.

Further, the expansion will be accompanied by a drop in temperature, which may affect materials-of-construction.

"Horses for courses."