Dionysia vs festival

Dionysia and festival both are nouns.

Word	Noun	Adjective	Verb	Adverb
Dionysia	Yes	No	No	No
festival	Yes	No	No	No

As nouns, festival is a hypernym of Dionysia; that is, festival is a word with a broader meaning than Dionysia:

Dionysia: an orgiastic festival in ancient Greece in honor of Dionysus (= Bacchus)
festival: an organized series of acts and performances (usually in one place)

Other hypernyms of Dionysia include fete.

Dionysia (noun)	festival (noun)
an orgiastic festival in ancient Greece in honor of Dionysus (= Bacchus)	an organized series of acts and performances (usually in one place)
	a day or period of time set aside for feasting and celebration