The first time they introduced the Eugenics Wars set in the 1990s, Spock called it the last world war. Pike in SNW elaborated that it was part of the escalating conflict that went nuclear as WW3 decades later.

they used to be separate wars, with the eugenics wars starting in the mid '90s and ww3 happening in the early-mid 21st century.

this has since been retconned, and the eugenics wars are now some time in our near future, serving as the starting gun for ww3