## 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][1] is *not* rerolled: "... you can use a bonus action on each of your subsequent turns to cause **this** damage again."
 - [Spirit Guardians][2] is rerolled each time there is a saving throw: "On a failed save, the creature takes 3d8 radiant damage ..."


  [1]: https://www.dndbeyond.com/sources/basic-rules/spells#HeatMetal
  [2]: https://www.dndbeyond.com/sources/basic-rules/spells#SpiritGuardians