What does epiphany mean?
The word epiphany means manifestation or appearance, from the Greek epipháneia, which is derived from the verb "to appear." When spoken of apart from anything distinctly theological or spiritual, to have an epiphany is to come to an understanding about the essential nature of something that might feel as though it is the most important realization that can be attained, perhaps even that the truth of it had been previously hidden.
Scripturally speaking, in the New Testament the word is used to describe Christ's birth, His appearance after being resurrected from the dead, and His Second Coming.
"Theophany," from the Greek theophaneia, is distinctly about God and how He manifests Himself to humanity.
Although one of God's attributes is that He is indeed omnipresent, a theophany is a temporary and sudden revealing of His appearance, and not an enduring presence.