While each state has a court that’s supreme, only 48 call their top court the Supreme Court; in Maryland and New York the state’s highest court is the Court of Appeals. To make it more confusing, in NY there is also a Supreme Court, but it’s a court of general trial-level jurisdiction, meaning that your case is likely to start in the Supreme Court and then go into the appeal system.
In that case, the supreme court in Maryland and New York is the Court of Appeals, and the Supreme Court is not the supreme court. (Note the use of lower case “s” and “c”.) Another example is that the supreme court in Australia is the High Court – Australia does not have a “Supreme Court”, but at least some of the states do.
Even Court of Last Resort is a bit of a misnomer. There defiantly are cases for whom a certain court would be the court against whose decision there is is no judicial remedy even when they are not the Highest court in the hierarchy. Or against whose decision review is very limited in scope.
Of course many Courts of Last Resort require a leave to be granted before appeal can even take place.