Classicism can be broadly applied to Ancient Greece and Ancient Rome, because of how often the sources intermingle (with many older Greek sources transmitted through Roman copies, and many Roman sources themselves written in Greek), but there's usually an element of specialization in one or the other for any given classicist.
I like the way we handle it in German, where Klassische Altertumswissenschaft is the study of Ancient Greece and Ancient Rome as pioneered by Friedrich August Wolf in the 1700s, and Altertumswissenschaft is used for the more broad study of antiquity.