The Holmes Basic Set (1977) is an introductory companion set to original D&D that anticipates AD&D in a couple places (there are several spells in Holmes that weren't in OD&D but were in AD&D, such as Tenser's Floating Disc) and goes its own way in a couple places (the aforementioned combat/initiative rules) but is closer to OD&D in both rules and feel than any other version. Like the more recent WotC Basic Sets, Holmes wasn't intended as a complete stand-alone game -- once you reached level 3 (which was supposed to take a dozen or more sessions, btw) you were supposed to move on to either OD&D or AD&D. The art in this set is by David Sutherland, Dave Trampier, and Tom Wham. This is my favorite Basic Set.
The Moldvay Basic Set (1981) is a revision of the Holmes book to make it more mainstream/kid-friendly, and to integrate it with the Cook/Marsh Expert Set (1981) (in place of the 1974 OD&D box, which was taken out of print at this time) to make a complete game, parallel to AD&D. The Moldvay Basic Set is probably the most streamlined and straightforward presentation the D&D rules have ever had, and the Cook/Marsh Expert Set is surprisingly close to OD&D. I don't really like the changes that were made to either the rules or the tone of the game in this set, and much prefer OD&D (supplemented by Holmes for novice players), but I do appreciate that this version succeeded in its goals of making the game more mainstream-friendly and kid-friendly and is likely responsible for D&D's mainstream success in the early 80s. The art in this version is by Erol Otus, Jeff Dee, Bill Willingham, Jim Roslof, and David S. Laforce.
The Mentzer Basic Set (1983) is a re-write of the Moldvay set which keeps the rules 99% the same but changes the presentation drastically to make the game even more mainstream and kid friendly. Moldvay's single rulebook is divided into 2 books -- a player's book and a DM's book -- both of which devote significant page-count to narrativized intros to the game in "choose your own adventure" style (the player's book presents two complete solo adventures that introduce the concepts and rules of the game, the DM's book gives a step-by-step script for how to run an adventure). This makes this set ideal for teaching the game to an absolute novice who'll be learning the game solely by reading the books, but once the rules are known its much less convenient than the Moldvay presentation. Plus, the tone is simplified to the point that teenagers and adults might feel condescended to. The Mentzer Expert Set (1983) is near-identical to the Cook/Marsh Expert set, reorganized to match the presentation of the new Basic Set, and with a few numbers changed to flatten the power-curve and allow for the higher levels detailed in the Companion (1984) and Master (1985) Sets. Those sets, in addition to covering higher levels (up to 36), also introduce new rules that can apply retroactively to lower levels (new weapons, new proto-prestige classes, weapon mastery (sort of a proto-feats system), etc.) the cumulative effect of which makes for a much more complicated game (perhaps not quite as complicated as AD&D, but close). The art in this edition is by Larry Elmore and Jeff Easley. This is the edition I started with (sort of -- I had a Mentzer Basic Set but a Cook/Marsh Expert Set).
The Rules Cyclopedia (1991) is a compilation of all 4 Mentzer sets (plus some additional material from the Gazeteer series and a couple new rules) into a single hardback book. It marks the only time since the original 1974 OD&D set that the game was complete in one volume (and even OD&D has 3 separate booklets in the boxed set). Cover art was by Jeff Easley; I don't know the name of the artist who did the interior art but it's very bland and uninspiring.