MSR stands for Molten Salt Reactor. It's a type of reactor that can use either Thorium or Uranium or Plutonium. For some reason a lot of people equate it with Thorium.
MSRE specifically refers to the Molten Salt Reactor Experiment [1], which was a reactor that burned only Uranium, never Thorium.
By the way, the Department of Energy is collaborating with the private industry on a number of advanced reactor designs [2]. There is only one molten salt reactor and that one uses Uranium or Plutonium, not Thorium (see [3], slide 3).
[1] https://en.wikipedia.org/wiki/Molten-Salt_Reactor_Experiment
[2] https://www.energy.gov/ne/articles/infographic-advanced-reac...
[3] https://www.nationalacademies.org/documents/embed/link/LF225...