Oh man, don't even get me started on 4e D&D! It was pretty different in a few major ways. I think it was an attempt to modernize the game and create a more consistent set of base mechanics for the game to run on, but it provoked a pretty strong backlash in the RPG community so 5e is very much a return to more traditional d&d, just streamlined and simplified.

4e had this concept that, at the core, all characters and classes should more or less use the same base mechanics, and they would just have powers or features that broke or elaborated on those base mechanics in some way. You can kind of think of it like something like Magic the Gathering. All decks at the most basic level work the same way, but the cards you use cause the deck to function differently.

4e had this structure of "Powers". Every character had At Will powers, which they could do any number of times per encounter, Encounter powers, which could only be done once per encounter (once per short rest), and Daily powers which could only be used once a day (once per long rest). Martial, Divine, and Arcane classes all got roughly the same number of these powers, so you didn't have some classes that just did one thing every turn (like the 5e Champion fighter just swinging his sword every round) and some that had a huge list of options (like a high level wizard or cleric). Everybody had pretty much the same number of options.

The other thing that was really different about 4e is that it practically mandated grid-based combat. Movement and distance were given in the number of grid squares moved, not in feet, although the grid was still assumed to be 5' scale, and things like opportunity attacks, forced movement, hazardous terrain, and AoE attacks and zones were much more prominent in 4e. This meant that a lot of spells and powers did cool, fun things with AoE effects or forced movement, or repositioning enemies or allies. It was a very tactical game.

The last thing about 4e that I really liked was that it was written in very gamist language. The designers used a keywords and mechanical terms that were kept very consistently defined, rather than the natural language approach of 5e. It meant that, even though it might take a little longer to grok at first, there was a lot less of the kind of rules-lawyering that happens with older editions of d&d and, to some extent, with 5e. It was a very tightly and consistently written and designed game. It's just unfortunate that it killed too many sacred cows of the franchise, and a lot of grognards just couldn't deal with how different it was. It wasn't without it's flaws, there was some pretty significant power creep, in particular with feats released in later splatbooks, and the math was probably a bit too vertical - by level 30 the attack bonuses were pretty absurdly high. But it had a really deep, very fun character building mini-game that just isn't present in 5e, and it worked really well at the table. That's not even to go into how fantastic their design was for Monster stat blocks and combat design.

Sorry for the wall of text, I really enjoyed 4e and I wish it hadn't died such an abrupt death. I like 5e fine, and I'm glad that it has gotten so popular and brought so many people into the hobby, I just hate that such a well designed RPG is sitting and collecting dust. I'd love to play another 4e campaign, but it's hard to get the band back together now that everybody has moved to different states and have kids.

To bring it back to the original topic, the reason I decided to pick up GloomHaven is that I saw it described as a "spiritual successor" to 4e d&d. it's got some of the same feel, with tactical combat and each class having unique powers. It's really been satisfying in some of the same ways that 4e was.