The RS125 Came with 2 types of engine from 1996 to 1998 Aprilia fitted the Rotax 123 type engine, and from 1998 to present day they fit the Rotax 122 type engine. Please note both the 122 and the 123 type engines are 124cc the 122 and 123 is reference to the type.
Now the confusion is around 1998 (the swop over year) you can not always rely on the date of registration as the bike may have been made in 1996 but not registered until 1998 and thus has the 123 type engine fitted.

So this is how to check what type you have.
All the engines have cast into the crankcases the type so this helps, but most engine get very dirty so it can be hard to find which one you have.
If you think you have the Rotax 122 1998-2009

Sitting on the bike best with the fuel tank up look on the left hand side of the engine next to where the cylinder is. On top of the crank case it should say “Rotax122” you may need to degrease the area to see this. 

 If you think you have the Rotax 123 1996 -1998

Look on the left hand side rear of the engine next to where the engine number is. It should say “Rotax123” you may need to degrease the area to see this. 

What are the differences between the 2 engines?
Clutch basket
The 123 clutch basket is held in the normal way with a nut (M18x1.5) on the centre hub, where the 122 has no nut holding the basket in. The 123 has the same clutch plates as the 122 but the 123 has 6 friction plates and 5 steel plates where the 122 has 6 friction and 6 steel plates.

Transmission
Not too much to know, they are 2 totally different gear sets and selector forks you cannot use any of the 123 in the 122 and vice versa. 

Gaskets
The crank case & clutch cover gaskets are different. There are 2 different type of centre gasket! it is important to identify which type you need as if you use the wrong one coolant will leak out between the crank cases, best to compare with the old gasket. The base gaskets are also different, but the head o-rings and reed gaskets are the same.

Crankshaft
They both use the same con rod that is about it, the 122 has the primary gear held on with a C-clip and the 123 has a Nut holding the primary gear on. They both have different tapers on the ignition side so you cannot swap the ignition systems around.

Balance shaft gears
They both use the same nylon gears; click here about timing them up

Cylinders And Pistons
They all use the same 54mm piston. The cylinders are different in a few ways.
Cylinders they use different stud spacing on the cylinder base see photos below. 
There are 3 type of 123 cylinder all fit the 123 but some are better than others. 

A: Really early 123 type cylinder has no auxiliary boost ports.

B: Same shape as above but with auxiliary boost ports

C: Now this is more like the 122 type casting but has the front studs the same width as the 123. Now you can mod this cylinder to fit onto the 122 by slotting the front holes to match the 122. The 123 cylinder uses 7mm studs and nuts to hold the cylinder head on.

Aprilia RS125 Engine Parts:

Info on how to set up the balance shaft gears Rotax 122 Type