The difference between Epiphany and Eureka

Epiphany is also noun with the meaning: a manifestation or appearance of a divine or superhuman being.

Eureka is also interjection with the meaning: an exclamation indicating sudden discovery.

check bellow for the other definitions of Epiphany and Eureka

Epiphany as a noun:

A manifestation or appearance of a divine or superhuman being.
Epiphany as a noun:

An illuminating realization or discovery, often resulting in a personal feeling of elation, awe, or wonder.
Epiphany as a noun (Christianity):

Season or time of the Christian church year either from the Epiphany feast day to Shrove Tuesday (the day before Ash Wednesday, the start of Lent) or from the Epiphany feast day to the feast of the Presentation of Christ in the Temple (see Epiphany).