Grimrock does, indeed, fit into the format. The Grimrock games are an example of one of the two broad, most common subcategories in that they have essentially real time combat/interaction on a grid, wherein the players, traps, monsters, and etc. can act on their own. If you go afk without pausing in Grimrock and there's a snail coming at you, it will eventually reach you and kill you without any input from you directly. I enjoy LoG a great deal, but it's not really my favorite scheme simply because it can lead to some really awkward juggling and strafing gameplay on occasion. It's not bad by any means. I just prefer to take my time.
The other most common format is essentially grid movement, just like Gridrock, mixed with "JRPG" style turn based battles. I put that in quotes just because the actual provenance of this particular mode of gameplay is more complicated than it simply being western or Japanese in origin. I suppose the whole Drpg genre owes the most to the old Wizardry games, which basically showcase the journey these mechanics took across the world, with Wizardry being a western game that happened to make it big in Japan and ultimately contributed to the genre fluorishing over there (while it largely stagnated here, until indie gaming started to sort of give it a bit of new life). Wizardry itself, the IP, was eventually bought out by a Japanese company, with the most recent installments being Japanese in make and origin.
But I digress.
The older Wizardry games featured "JRPG style" turn based combat. I haven't played all of them (and none of them to completion), but I think most of them were turn based? Wizardry 8 is a departure to some extent in that it uses a sort of hybrid "real time with pause" sort of system. Anyways, a lot of DRPGs use that combat paradigm to the this day, with the more real-time variant being less common, as far as I can tell. Sometimes it's got random encounters, sometimes monster icons roam the map and you gotta collide with them to initiate turn based combat, sometimes it's a mix, and of course the actual combat mechanics can vary widely once you're in it, but the core is very much the same.
There's a third possibility I see occasionally (and have played around with designing myself) that's more akin to the old school Rogue style of movement and combat. Basically, enemies, traps, and the player move on the grid, just as they do in Grimrock, but every movement and action takes a "turn" and standing still does not progress time. So enemies only move when you move, basically. I am bit more of a "turn based JRPG" girlie myself, but I also like this modality quite a bit, since it combines the added immersion of the real time format with the ability to take your time and strategize.
As for which one is easiest to make, well ... I've tried them all in my time, and I honestly can't say ... they all have their own pitfalls and challenges, and I imagine it might vary widely from person to person. One nice thing about taking the turn based JRPG approach is that you don't have to implement pathfinding AI and such, so that's probably what I'd generally go with in a time crunch scenario.
But, yeah, as to your question, examples ...
For real time, I wouldn't really recommend going too far back (or too hardcore old school) if you're new, simply because that experience can get quite rough and frustrating. The more user friendly and modern Legend of Grimrock games is about the best bet. If you're looking for more of that, the Vaporum games are pretty great in most aspects. I haven't played Lockdown yet, but really enjoyed almost everything about the first one ... besides the writing and the story, which were competent but just not to my taste. The dungeoneering, encounter design, combat, puzzles, were all very enjoyable in it.
To check out the turn based variant, well, there are a lot of options ... Again, I probably wouldn't recommend going too far back, but you wouldn't have to, as they are getting made to this day. Unfortunately, since they are a bit of a niche within a niche within a niche, the newer ones tend to get released for AAA prices or close. I had a fabulous time with Undernauts, and absolutely loved Labyrinth of Refrain and Labyrinth of Galleria, and I think all of the above are fairly accessible for newcomers, but of the set, only Refrain, being the oldest of the three, is particularly affordable, usually sitting at just under 20 bucks. You may want to try and catch a sale, or maybe pick up a physical copy somewhere second hand, if you can. I obviously think it's worth supporting these studios because, you know, I happen to love this subgenre and want more of it, but money is hard, and if you're not sure what you're getting, or if you'll even like it, it can be a tough sell.
Going slightly older, Shin Megami Tensei: Strange Journey Redux runs very well on Citra ... though OF COURSE you'd first have to own a physical copy of the game, OOooobviously (either way, Atlus isn't exactly going to be hurting for cash any time soon, and DS and 3DS game access and preservation are a mess, so, you know, do with those opinions what you will).
And, of course, there are a ton of fun, free examples made by participants of this very jam in years prior.