HERMS is : Heat Exchange Recirculating Mash System
RIMS is: Recirculating Infusion Mash System
You see both types of systems, but more and more people are doing HERMS. This is because with the HERMS, your output from the MT goes through a copper coil that sits in your HLT and is surrounded by water at your given mash temp. This is desireable because the only heat your mash sees is what you expose it to in the coil. With a RIMS, the recirc from the mash is generally directly heated and this can cause over-carmelization, etc.
In either method, the continuous recirculation produces clearer wort.
I can only speak for myself, there are people who are happy with both methods...but I plan on installing a HERMS system in my rig.