Greek epic poetry is long-form, in dactylic hexameter meter, and involves the goings-ons of Greek heroes and/or the gods. Its written form is the culmination of earlier, orally-transmitted tales which involved familiar smaller tales of gods and men, woven together by the skillful rhapsode into larger tales. The nostos of Odysseus, for instance, involves many discreet episodes which the poet has spliced (the Cyclops, the Lotus-Eaters, the witches, the contest of the bow, the Phaeacians, etc). Epic is generally older than lyric--the first tales were probably being written down in some form by 700 BCE, and the Homeric epics as we have them today were solidified by 500 at the latest.
Greek Lyric is a little later, though its oral origins probably reach back into the "Dark Ages" of Greece just like epic. "Lyric" as a group is really a hodgepodge of genres which are neither epic nor drama. In general, lyric is much shorter than epic, and tends to focus on more personal concerns. Within "lyric" are songs meant to be performed at sacred rites (the Partheneia, e.g.; love poetry (Sappho, Archilochos); poems written to praise athletes or other famous people (Pindar); short-form mythological tales (Bacchylides, e.g.); short exhortations to battle, or to performing acts of valour (Alcaeus); performative invective against real (or imagined?) social opponents (Archilochos). These diverse songs are called "lyric" because they were composed to be accompanied with the lyre, and they are often called "poetry of the occasion." There are many subdivisions, encompassing many subjects, forms, tones, and time periods from roughly the 7th century to the beginning of the 5th century BCE.