On kissaten - 店 ten is the kanji for "store", though you might also learn 屋 (ya, lit. roof). kissa means consume tea (喫茶), more or less. I didn't notice them on my first visit, I wasn't into coffee then, but they're everywhere and a really nice way to get breakfast (egg toast + siphon filter for a few hundred yen). Not necessarily the best coffee in Japan if you don't like dark roast, but it's often made to order and not out of an urn.
Izakaya I would associate more with drinking and small plates of food, but not necessarily a catch-all for bars.
YMMV I guess, but I found the best coffee at kissatens, and I hate dark roasts. Lots of great, sometimes super tiny, third-wave pourover types, too. But I guess Japanese coffee culture is more about evening consumption since there were many that were open at 10PM or later, but very few open before 10AM.
I can see espresso cafe culture spreading a bit through Japan, with australian style cafes offering great espresso and mixed cuisine on the menu. I think japan/australian cafe culture colliding has been an incredible thing. It's happening in Australia too, where the Japenese aspects of small inexpensive foods are mixing into Japan influenced cafes here.
I think Australia and Japan have a surprisingly symbiotic cafe culture that's betting blurred together.
I think it's the only place I've been in my life where the coffee actually tastes like the tasting notes say it does. Even when they say "mojito", which was surprising.
I agree about Glitch, though it gets super busy. There are cafes which also serve their beans if you don't want the wait. I would also recommend Fuglen's tasting experience in Sangubashi. It's a bit theatrical, but great if you want to try something a bit different.
Izakaya I would associate more with drinking and small plates of food, but not necessarily a catch-all for bars.