The Atelier games are basically turn-based JRPGs combined with an alchemy simulator. The general setup is you have a few years to perform certain tasks--in Totori, you're trying to get your adventurer license and find out what happened to your mom, who was also an adventurer--and you do this by crafting items, taking quests and fighting monsters. The battle systems, while competent, are secondary in nature; the real star is the alchemy stuff, which involves gathering ingredients and combining them to create items for quests or to use in battle (which, if you're good at alchemy, eventually overpower the damage you can do with weapons by a lot).
The closest analogy I can think of is Recettear, minus the shop management aspects and plus the alchemy. Recettear is actually the reason I got into the Atelier games; the franchise was the only thing that seemed close to what Recettear had. But the production values are a lot higher and there's a lot more content--we're talking 30 hours for a first playthrough at least.
Ys is an action RPG, very fast-paced. They have a reputation for being balls hard--I died so many times to the first boss in Ys Seven (which you encounter half an hour into the game!) that I stopped playing the game for a while after I finally beat it because I was afraid of what would come next. Turns out it's not so bad, you just need to master the dodge/rolling moves and stuff like the flash guard to block damage and whatnot. Ys is a game I've always associated with mobility above all else--I was rolling and dodging all over the place, and it's a ton of fun. There's no overworld per se; rather, all the areas you go to are connected to one another, so it's like the game is nothing but overworld (but with level transitions).
I'm not sure what to compare it to, exactly, as most of the action RPGs I've played aren't this fast. Some people have compared the Ys series to Zelda games but personally I don't really see it, as they're not particularly heavy on puzzles and it's really about the fighting. Hopefully I gave you a decent idea of what to expect, though.
