In our lab meeting we were chatting about divergent selection. I was confused at some point because I wasn't sure what was the meaning of this work in comparison to diversifying/disruptive and other types of selection.
I think you are conflating selection and evolution. Diversifying selection is when the variance of a trait in the population increases and even potentially becomes bimodal. This may lead to divergent evolution, i.e. a speciation event. Whereas directional selection still leads to evolution but not necessarily a the formation of a new species.