Illustrations are art pieces which could be done both digitally and traditionally, with the purpose of illustrating(demonstrating) a scene or character in a particular situation. This is usually an extremely finished-looking work made for sales and promotion.
Concept art is not exactly art in the traditional sense, it doesn't need to symbolize or imply on certain motifs. Instead it's made as part of a decision process for how a certain part of a game/movie/book/etc would look like. They are usually made in the dozens, what you usually see posted on art sites is usually the final design, after it's approval, so not everyone knows what goes on behind the scenes.
CG = computer generated. It's an oldfashioned term for digital art that still sticks around. It would be like having a digital art digital art subcathegory. Concept art is development art done to figure something out before production. Be it a game, movie, whatever. It isn't just digital art, albeit its very common since production pipelines are tight and digital art has a lot of advantages with time and revisions in mind. Illustrations are again just not a digital at thing. An illustration is a piece of art that is a part of something, like an picture in a book, or on a game card, a cover of a book or magazine, etc.
Digital art is art generated by a computer and users inputting data to do art. Basically art that involves computers and touch-sensitive digital devices to work. So technically there will be a whole lot of categories and all, as does traditional art and their counterparts. but all it matters is that! It's either digital or traditional.