"FH" is the designation for a MOSFET unit. This is what you want.
"SH" designates a Shunt style unit. While they work OK, they will run a bit hotter (or a LOT hotter!) and normally not work as well as a MOSFET.
The differences between the way these 2 types operate is best left to the electrical geeks here. If you need to replace, get a MOSFET.. No harm in getting one that is not model specific. Lots of us use R/R units from other bikes, and mount them under the seat. A MOSFET unit barely gets warm, so it can be mounted out of the cooling airstream. They will also have an extra wire, compared to the early OEM units. The ground on the early ones runs through the frame to battery. Newer ones have a ground wire. Run the red and black wires from the new unit directly to battery, soldering any wire splices you have to make. The 3 wires to the stator can be soldered also - remove the 3-prong plug if you feel confident in soldering these wires. This plug is a famous trouble spot. Corrosion here causes heat, and the plugs have been known to melt.. The 3 wires are carrying 3-phase AC, so there is no incorrect way to hook them to the R/R.. If you don't want to solder them, get some POSI LOCK connectors, and slip a bit of heatshrink over them to keep them from getting wet.