I learned this from a Vsauce video YEARS ago, and for some reason, I remember this concept vividly alongside the brachistochrone.

A Tautochrone is a curve where, no matter at what height you start, any mass will reach the lowest point in equal time, again given constant gravity.

On the other hand, the Brachistochrone is the path between two points that takes shortest to traverse given only constant gravitational force.

Actually, mathematically, they both are the same curve but they arise from slightly different but related problems.