MOO and CoolMUD/ColdMUD are very different than mushes; different assumptions and the hardcode presents a very open-ended set of tools. Numerous people (including me, sigh) have used MOO to e.g. write a webserver and other oddities. This is wonderfully powerful, but also means that the MOO user interface is a lot less unified. The bare minimal.db setup doesn't differentiate between players/things/rooms/doors; all of these things are softcode. I think this is fantastic, but it also means the average non-technical user can't really tell much about the UI from knowing only that site Foo is "a MOO."
MUSHes (and MUXen, which really are the same for these purposes) instead present a very uniform UI with (relatively) rigid constraints on the data and implementation choices. On the code-side of things, ALL data is LBUFs, or large-buffers, which traditionally were 4000 bytes in size. More modern MUX environments generally default to 8000, Firan used 24000, and my fork (in use on the Reach, Darkspires, et al) tends to use 64000. MUX use utf-8-based, so that may or may not mean 64000 characters tho. Also, color-codes are stored in-text in a persistent fashion. All other datatypes-- integers, floating point values, lists, error indications, DBrefs, etc.-- are represented in these text LBUFs with the same hard limit on sizing.
MOO instead had an actual typed (albeit dynamically typed) language with internal stack-oriented bytecode virtual machine. MUSHes lack that data typing capability, which is why larger mush applications like Anomaly Jobs (a ticket tracking system, essentially) tend to have hilariously small limits on their dataset and prefer to drop data as soon as possible.
To get an idea of MUSH programming, read Amberyl's guide and likely browse Brazil's tinymux softcode wiki, if that is still up. The PennMUSH people also likely have some good docs. For most users, the "big four" mush families (TinyMUSH, RHOST, PennMUSH, and TinyMUX) are essentially the same, though they have different design goals and limitations, and somewhat different UIs for email and comchannels.
To get an idea of MOO progamming, I actually mirror some of the MOO hardcode and semi-standard default softcode starting point, aka a 'core,' which explains some of the basic MOO user assumptions, as far as they ever had any.
There is also MUCK. Where MUSH went with a naive string processor and MOO went with a modern yacc parser with bytecode stack vm, MUCK implemented a typed FORTH, accessible in-game as MUF and a more limited higher-level MPI language sometimes used on top of that. MUCK is a great deal more powerful than MUSH, but many people have trouble thinking in forth terms and MUCK has historically been associated with the Furry community. @nuku_v would be a good person to ask about that stuff, but he doesn't seem to have connected here in a few months.
MUSH/MUX examples this community is likely more familiar with, vaguely sorted by max-conn per last 30:
- Shangrila (adult)
- The Reach (hybrid NWoD1+NWoD2 set in Maine with Lovecraftian theming), many staffers/players here
- Naughty Muffin (adult)
- City of Hope (wod?)
- New Prospect (wod?)
- Kushiel's Debut (Kushiel books)
- M*U*S*H (Penn-based social)
- HeroMUX (superheros)
- CoMux (superheroes)
- Requiem for Kingsmouth (wod)
- Sheltering Sky (wod)
- Eldritch (wod; are you guys even open yet?), @thenomain's game
- Shadowrun Denver (shadowrun)
- Road to Amber (amber)
- PernWorld (pern)
- DarkSpires (Dresden Files, FATE-based, set in Oxford), @jinshei's game
- RenoMush (wod)
- Blood of Dragons (GoT)
- Game of Bones (GoT)
- City of Fog and Blood (nwod, sadly mostly defunct)
- Haunted Memories (nwod, set in Vienna, sadly defunct), many staffers/players here
- Wildcard (AnitaBlake, FATE-based, basically defunct), formerly mine, now run by @Cobaltasaurus, in theory
- Blood&Citrus (AnitaBlake, NWoD1 retheme, defunct)
MUCK examples:
- Tapestries (like a furry shangrila)
- Furry Muck (similar but less adult more social?)
- Flexible Survival (MUD-like but very adult, furry), @nuku_v's game
- Rusted Promises (Still a bit MUD like, but more RP-oriented, not really adult, somewhat furry), also @nuku_v's game
Be sure to look down the lists at mudstats, as there are many more than I have listed but I've been a bit out of touch and don't recognize a lot of the newcomers. Note that they separate MUSH/MUX and don't separate NWoD1/NWoD2/OWoD, so it's a bit awkward.
Also, be sure to check max/min/avg/current orderings; some games are in different timezones (e.g. because their staff are in Austrailia), and have varying numbers of continuously-connected or continuously active clients. Reach's internal +who at least gives a stat on currently-active unique IPs, which is a more meaningful number.