Historically, the term "reporter" described the individual person who compiled, edited, and published volumes of case law. Now "reporter" refers to the published books containing judicial opinions. Below are three sources where you may access reporters of United States Supreme Court opinions.
How do you find the docket number for a case? You can search https://www.oyez.org/ using the party names (ex. Roe v. Wade).
Why search by docket number? You can search by party names, but sometimes this will lead to confusion. Docket numbers are unique to specific cases.