* The Greek language: A language belonging to the Hellenic branch of the Indo-European language family. It's spoken in Greece and Cyprus, as well as by diaspora communities worldwide. There are both modern and ancient forms of the language.
* The people of Greece: The citizens of the modern nation of Greece, or more broadly, people of Greek descent.
* Ancient Greece: A civilization encompassing various city-states and cultures which flourished in the Aegean region from the Bronze Age through the Classical era (roughly 2700 BCE – 146 BCE), known for its contributions to philosophy, democracy, art, architecture, and literature.
* Greek culture: The collective cultural heritage, including traditions, beliefs, arts, and values, associated with Greece, encompassing both ancient and modern aspects.
To understand what someone means by "Greek," you need to look at the context.