There seems to be a difference of opinion on the WWW about the meaning of 'wade', varying from ankle to neck deep. Some say only walking in ankle-deep water is considered wading, others seem to think you're wading until you're neck-deep in the water.
And if you're wading only until you're ankle, knee, or waist deep, then what do you call walking in the water that is higher than that?
In british-english, Wading means walking in water that is deep enough to require some effort to walk through. Water that only comes up to my ankles is probably not deep enough to be considered "wading". Provided that you are walking (and not swimming or submerged) it can be called wading.
British English uses "wade" figuratively to mean "do something with difficulty", eg "I had to wade through 500 pages of legal reports before I found the case I was looking for".
In american-english it tends to be used for shallower water, and in situations that British English speakers call "paddling". There is quite a lot of overlap between the American and British uses of the word: "They waded across the stream" would correct in both dialects.
To complement James K's answer, you asked what term to use when the water level is higher than wading level.
I don't know of any other term that means to walk through water, so if the water level were higher than wading, it's just "walking through water", possibly including some expression about the height of the water, like "at chest height", "at waist level" or "knee deep".
If it's above your head and you're still walking, then it's "walking underwater" or "walking on the ocean floor/the bottom of the lake".
