MRS is the demand side of equation while MRT is for the supply side.
MRS defines how much a consumer is willing to give up of good X for 1 additional unit of good Y to stay on the same utility level. It is shown by indifference curve. MRS = Price of X/ Price of Y
Similarly, MRT is how much a supplier is willing to give up producing good X for 1 additional unit of good Y. It is shown by Production Possibility Frontier. MRT = MC of X/ MC of Y
