I must limit the scope of this discussion to the non-moving static stuff that can be painted, printed, drawn or tooled onto paper or watched on computer screens. Everything below are only opinions.
Image is the most general concept. It's anything (printed, drawn, made with tools, painted, an onscreen pattern) that can be considered to be created, not appeared without anyone's intentional effort. If a television screen shows some random electronic circuit noise that's not an image, but if someone has intentionally grabbed a screenful of the same noise, that's an image. There's no image without a human intention to catch or make by himself something visible.
An image can be an image with no intentional relations other than the existence or it can present something. The latter means that it contains some intentional relations between the parts of the image or between the image and something outside the image. The relations can be real and verifiable or they can exist only in some imagined context.
A graphic artist creates images. He draws, paints, throws paint, shoots holes to a surface, uses computer software etc... It's well possible that his image presents nothing in his mind or in his speech or both, but some watchers see this and that or they say they see this and that. They can say it for their own intentions to get some power. This is how geniuses can be also made instead of being born with abnormally capable brains.
Ordinary people with no artistic intentions or talents also create images. They often have a good reason for it, for ex. to show what they have or want.
Back to the subject. An illustration is an image which presents something which is said also as text, illustration is a part of a work which contains images and text, it cannot exist without text. The relation between the text and the image can be undefined, it's enough that someone can see some connection.
A figure is an illustration which presents a single relation or multiple, but strictly defined relations.