It depends on the spell
The exact wording of the spell will tell you when it does damage and if it is the same damage or needs to be rerolled.
For example:
- Heat Metal is not rerolled: "... you can use a bonus action on each of your subsequent turns to cause this damage again."
- Spirit Guardians is rerolled each time there is a saving throw: "On a failed save, the creature takes 3d8 radiant damage ..."