In order to reach the Supreme Court, a case has to work its way through the (1) trial court (District Court, possibly also a state court) and (2) the Court of Appeals. One of the parties then (3) petitions the Supreme Court for a hearing and Court either (4) accepts or denies the petition with a writ of certiorari (abbreviated Cert in a citation). Along the way, changes might be made to some feature of the litigation, such as (5) change in counsel, (6) a party joining the litigation, or a (7) separation of issues, and each of these results in a document published in Westlaw and the print reporters. Documents such as these are called memorandum decisions and are indicated by (Mem) in a citation. A case like the one described here would generate at least 7 documents in addition to the final judgment, and all the documents would have the same case name. How do you know which one you want?
When you get a long list of what appear to be identical cases, look at the information under the title.
In the example below, a case name search for Campbell v. Acuff-Rose resulted in 6 documents. Of the 3 displayed in the illustration, which one is the Supreme Court case we're looking for?