Landscape words are always a bit fuzzy, and can be used differently in different regions. Generally, I'd say that all gorges could also be called ravines, but many ravines aren't gorges. A gorge contains a somewhat significant body of water (at least a large stream) flowing quickly through large, steep mountains. A "ravine" is just any long valleylike or even ditchlike thing. You could say something like "several dry ravines ran across the farmer's field". Again, a ravine can be as big as a gorge or a canyon, but it can be much smaller, and it can be dry. | "Ravine" can also be used to refer to a crevasse in a glacier. In general, "canyons" will be in a desert, and will have very steep walls separating a river from a flat plain above it. In the Appalachians, gorges are often called "hollows". I'm sure that other places have their own regional words for similar landscape features.

Both are formed by water and can have a river / stream at the bottom. The words can be used interchangeably in most (if not all) circles. I'm only saying 'most circles' because there may be a very specific, technical difference between them, I can't guarantee, but I don't think so! If there is a difference, most people don't know it and wouldn't know if you used the wrong one. If you are writing something for scientific purposes, please wait for a more qualified answer!

Overall, I agree with Chris' answer. In the Pacific Northwest, though, there are gorges that could be called canyons but not ravines, e.g. the Columbia River Gorge. Subdivisions of my city are separated by "ravines" which have seasonal waterflow. No one would call them gorges.

Thank you!

These Wikipedia pages might be helpful: https://en.wikipedia.org/wiki/Ravine https://en.wikipedia.org/wiki/Canyon ("canyon" is apparently synonymous with "gorge", though I'd expect a canyon to be bigger than a gorge)