The difference between Tummo and Wim Hof's method is just like between Zen and corporate mindfulness. As for Tummo itself, it's not one method but a family of different practices differing from one another on various points. Many of these use very different breathing methods that Wim Hof is using. But the most important difference is that the main point is completely missing. It's like, I don't know, practicing calligraphy of Shakespeare's plays without understanding a word in English.

I know the WHM. Wim himself claims that the WHM is not tummo.

And with good reason, it isn't. It might use similar breathing techniques (vase breathing seems to be similar to one WHM breathing technique) but that doesn't make the WHM tummo.