The truth is that reality is stranger than science fiction, and when you look at non-FTL travel you start to think about pretty wild and massive concepts that are done on the scale of thousands or hundreds of thousands of years. Even without FTL, if you built enough generation ships around our star and then fired one to every single suitable star system in our galaxy at the same time, it would only take just over 100,000 years for all ships to arrive and for the galaxy to be colonised.

"Generation ship" really depends on how fast you shoot it out of the system. If it's going fast enough it's not a generation ship from the passengers perspective. They'll arrive in 100,000 years but for the passengers it could be less than a lifetime of subjective time, plus and on the scale of the universe, 100,000 years isn't a long time. Supposedly it 100,000 years for our ancestors to leave Africa and settle all corners of Earth.

It just means that without FTL we all become time travelers while in transit.