What two types of jurisdiction does the US Supreme Court have?

This question has two possible answers as there are two sets of two types of jurisdiction.

One is that there is original and appellate jurisdiction. Original jurisdiction is where the court hears the case at the trial level. Appellate jurisdiction is where the court hears only an appeal from the trial court.

The other answer is "in personam" jurisdiction and "in rem" jurisdiction. "In personam" (Latin for "over the person") jurisdiction is where a court has jurisdiction over the persons involved in the lawsuit and is empowered to deal with matters between them. This occurs where a party has filed a complaint and the other party has been properly served with a summons. "In rem" (Latin for "over the thing") jurisdiction occurs when the court has jurisdiction over the particular thing the lawsuit involves and is empowered to deal with all issues involving the thing. An example is where the action is to partition a piece of land or to quiet title to the land or to foreclose on a mortgage. The land is located within the jurisdiction of the court so the court has jurisdiction over all matters involving that land.