I will throw Brew In A Bag in there too.
3V/3 Vessel is - I believe - inspired by commercial breweries. Each vessel can be designed, constructed and managed independently. This includes filling, heating, mash, boil, cleaning.
I mention this because 1V and BIAB means you do have certain "limitations", in that you are fixed to brewing in a fairly linear fashion and in a certain way. Most things have very easy work-arounds though.
3V is typically the most expensive, heaviest and hardest to clean. HERMS typically operates as 3V, though RIMS is flexible enough to work on 1V, 2V or 3V.
HERMS is arguably the most elaborate brewery type and is very popular for hands on people who like to fiddle. It pumps wort through a coil sitting in hot water, which is controlled to achieve and maintain each mash step. The coil in water is the heat exchanger, and the hot water is heated/controlled with an element.
RIMS is a simple version, which has the element directly in the stream of recirculating wort.
Both RIMS and HERMS use an initial infusion, then use external heat to hit and maintain temperatures. If you don't have an element you need to consider heat loss and volume as you add hot water to get each mash step, which has diminishing returns - so infusion is best suited to single step.
Each system has positives, negatives, "must-do"s as well as things to be aware of. AHB is a great resource for any questions you have.