Some folks may follow the rule of 4%, some perhaps as high as 5%. For those who don't understand what this means is that you don't want to withdraw more annually than your typical annual return.
So... the inverse of 4% (0.04) is 25. This basically means your total nest egg (capital) should be at least 25x your annual spend/budget. So if you want to spend $60k/yr (before) tax, then 60x25= $1.5MM required. Of course if you get pension, OAS, CPP then that also affects your magic number. I'd love to have more than $100k annually in retirement however that's unlikely.
Rich vs Wealthy? Rich may still have a rough budget, whereas Wealthy really can spend a few $100k yearly without any concerns of drawdown. An arbitrary number would be ~$3-5MM versus $10MM+ respectively.
Here's an excellent website (which I've posted before) that lets you go down that rabbit hole of estimating your spend as well as acturial-based review of your investment odds, lifespan, etc... quite a few other links on this site that are awesome:
https://engaging-data.com/will-money-last-retire-early/