Sorry, DJ is Datejust.
I would put watches with buttons and numbered bezels in the tool watch catagory, these were meant for serious duty, not tennis at the club.
Sport watches historically have been watches meant for a more active lifestyle, made of steel, waterproof, robust in construction, shock resistant. The Connie and earlier (non-dive) Seamaster’s both fit this profile (even their solid gold variants fit in this catagory). Dress watches were historically made of gold, slim in profile and elegant- water resistance optional as you are more attentive washing your hands in French cuffs anyway.