They made changes to stam for running (not only for characters but for mounts) for - hmm, Scalebreaker maybe? Anyway, yes, it's somewhat different now.
If you're playing on console, it was changed with this week's patch. You can run further on foot and mounted, but mounts don't sprint run forever anymore even when they've run out of stamina anymore.
...Glad I did all the Cyrodiil skyshards before the change is all I can say with that.
If you have the stamina on your mount fully leveled the change is awesome as you can ride a huge distance before running out and don't have to worry about getting dismounted by the first thing that hits you. On characters without fully leveled stamina it's a giant pain in the a$$ as you'll constantly drop out of sprint and have to wait a few seconds while stam regens enough to sprint again
One of the lesser spoken about changes but its SUCH a great QoL change... mag characters were so slow but now its much more tolerable sprinting on a non stam character. GG from me