Reddit mentions of Tornadoes! (Scholastic Reader, Level 4)

There's no hard definition for those terms, but I generally see "deadly" for what seem to be strong tornadoes vs. "damaging" for weaker ones (though really almost every tornado has the potential to be deadly in the right situation).

As for weather books for kids, I recently bought for a couple of my nephews that were really interested in weather a book called Tornadoes! in a series of weather books published by Scholastic, and they love it. It was actually a book I read when I was in second grade that I used to read repeatedly. Interestingly, it's surprisingly scientifically accurate (at least for the time period and for a book for kids). Admittedly, though, it's not as well-written as I remember, but it has cool illustrations and whatnot. You might have luck checking out other books in that series as well.

Also, the reading level might be a bit more advanced, but I also loved reading a book called the Handy Weather Answer Book when I was a kid (though it was an older version of the book). It's really just a book of weather facts, and it also has a lot of great pictures, etc. Again, it might be a bit higher of a reading level, but as a kid that loved weather, I used to practice reading it with my parents almost every night before going to bed.

Hope this helps!