I want to buy aikidogi but I'm not sure whether judogi and karategi can also be used.
Are there any differences between karategi, judogi, and aikidogi?
tl; dr
Buy what the other people in your club buy.
There are variations from brand to brand and art to art. I've done aikido in an aikidogi, a judogi and a karategi; none of them really affect my technique; they do affect my comfort. The big issue is how well it fits, and how reliable the brand is at selling equipment that fits. When I wear through my current gi, my next gi will match that which my training partners wear.
Before I answer, let me point out that the terms are not standardized; I'm just going to refer to trends/clusters. I own one karate gi, one gi that people describe as a judo gi and I've worn several aikido gi's past the point of safety.
In general, aikidogi are made of a loosely woven but thicker fabric, and the seams and edges are heavily reinforce. Many aikido techniques involve grabbing the lapel of the gi in order to control the body; you don't want that lapel to rip off in your hand and send your partner on an unplanned ballistic trajectory.
I'm told that aikido gi jackets are longer and the sleeves are a bit shorter. (but I've always wondered if that is a back-formation for the differences in stature between Japan and the West.) I know that my current gi is woefully short for my trunk.
Pants tend to be reinforced at the knee - aikido involves a lot of seated/kneeling work. Pants will also frequently have two loops to secure the drawstring. I'm not sure how functional this is, but there are techniques that involve pulling the pants, and the double loops may give more security
I don't play judo, but I do play Tomiki aikido, which is heavily influenced by judo. Judo gi and aikido gi are very similar - effectively interchangeable. As I said, I'm told that the judo gi is shorter through the trunk and may have longer arms, but that may just be style or one manufacturer. Judo involves a lot of stress on seams and lapels, so once again they're heavily reinforced.
I don't practice karate, but I wound up buying a karate gi in the hopes that it would be lighter for summer wear. Although it is technically lighter, it is more tightly woven, so it wind up being actually warmer. The seams/lapels are reinforced, but nowhere near as much as either of the other gi's.
There are strings on the lapels that anchor them to the opposite side of the coat - keeping the coat closed even if you lose your belt. Alas, because of some fit issues, these are actually counterfunctional for me. The coat is so long that if these are tied, they constrain my legs and prevent me from assuming deeper stances.
What you didn't ask, but I've learned is that the brand for my current gi is short - it keeps creeping up above my best and getting loose. I wish I had another six inches of length. The karate gi is so long that I feel like I'm wearing a narrow skirt. Listening to others in my dojo, there are brands that are reliable - when you buy a 4, you get a size 4, and there are brands that are unreliable (order a size 4, get something that is labelled size 4, but is obviously closer to a 3). That is why I urge you to consult your training partners, and ask them what they buy and how it fits.