They are 2 separate wars. There is a pretty good timeline on Wkikpedia.

Bro I did not notice this was a startrek com and was very confused for a second. Thought I missed something

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

i take it to mean that the definition depends on how you've learned about it.

a real world example is world war 2: if you're an american it started in 1941; meanwhile if you're chinese, it started in 1931; and if you're swiss or scandinavian it lasted until the 1950's

even in the same country it can be different, another real world example is the mexican rebellion of the early 20th century. if you're a religious/social conservative it went from 1921 to 1933; if you're not, it went from 1921 to 1923 and then there several followup wars like the cristero rebellion that lasted until 1933

conflicts don't cleanly start and end; they windup and then winddown slowly and it's up to you to define where the start and end are; and since we're all have different definitions, others will have different dates.