Both mathbbm and mathbb are wrong for number sets. These fonts look like the blackboard hack that you use to simulate boldface using chalk. On a computer you don't have this problem and you can simply use mathbf (actual boldface).
It's quite common to see \mathbb{R} used for the actual set of reals, while \mathbf{R} means a totally ordered field (i.e., an abstract object behaving somewhat like \mathbb{R}). The distinction is deliberate and the notation is good.
Better question: why use it, when you can use the real thing?
Mathematicians concerned by typography universally use real boldface. For example: Terrence Tao's blog, Donald Knuth, Paul Halmos (author of "how to write mathematics"), and the famous journal "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography. They use real boldface for the number sets N, Z, Q, T, R, C.
I've never seen a boldface R to mean a set different than the real numbers. Maybe this is some fringe custom in model theory, but in mainstream mathematics it has a clear and standard meaning. Can you point me to a paper where they use a boldface R with such a meaning (i.e., different than the reals). I'm sure that this usage would always be accompanied by a clarification to avoid any confusion.
That said, I still feel that I've seen every \mathbf letter used for something other than a standard number set somewhere. But probably not in the mainstream.
(Also, admittedly, I like the look of these letters.)
[1] https://arxiv.org/pdf/1611.07441.pdf
[2] https://annals.math.princeton.edu/wp-content/uploads/annals-...
(if we are nitpicking about typography...)
Sorry about that. A common typo. The keys are like right next to each other.