When should one use/not use overdrive?

I recently got a newer car and it has the overdrive button on it. I read the other questions regarding this but they didn’t address what I want to know, which is; do I need to use this for city driving? As I understand it, (and I use the term “understand” in its loosest possible sense!) overdrive is just 4th gear. So it seems like start/stop driving would be less of a problem or work on the engine if one only had three gears to contend with. But I realize that my understanding of things in the physical realm can be a bit fuzzy, so I stand ready to be corrected.
City driving with overdrive engaged; yes or no?
Friendly banter is appreciated, arrogant condescension – not so much.