Mouthguard or nightguard for teeth grinding?

They are the same: Interchangeable words for the same device. A well-fitting, dentist custom made mouthguard is a device that will either allow you to continue to grind, but instead of tooth vs. Tooth wearing down, you will have tooth vs. Mouthguard (which is softer than tooth & will wear instead of tooth). This will also act as a "stress-breaker" and in some people wearing it makes them stop grinding.

Also: There are over 100 designs and only two will reduce clenching or grinding, also called bruxing. The other designs will increase the bruxing or just protect the teeth and joint. The two that work best are custom made by a dentist and the store bought appliances will not reduce the bruxing. As with everything there can be some side effects that you need to understand with the appliances.

Same: Night guards should be made well and fitted properly by a dentist. The self made mouth guards bought at the stores can cause more harm. I.E.Tmj problems.