re "what models people like to explain": There was some good discussion of lepton universality violation at the end of the announcement talk.
tl;dr - electrons and muons are leptons, but what if they don't interact with photons the same way? (ie the rules of physics aren't universal to all leptons)
it is also important to note that due to experimental constraints and the nature of quantum mechanics different possible processes interfere with eachother.
eg: (a+b)^2 = a^2 + b^2 + 2ab
That 2ab is an interference term so a different process can get mixed in (quantum mechanically speaking). And we may not experimentally be able to disentangle it.
tl;dr - electrons and muons are leptons, but what if they don't interact with photons the same way? (ie the rules of physics aren't universal to all leptons)