God became man and that man was Jesus Christ.
The Incarnation was permanent, Jesus was fully man and could die just as we do.
A theophany, on the other hand, is a temporary manifestation of Jesus in another form. For example as the Angel of the Lord.
Here is an account below where Jacob wrestles with God.
Genesis 32:24
Then Jacob was left alone, and a man wrestled with him until daybreak. 25 When the man saw that he had not prevailed against him, he touched the socket of Jacob’s hip; and the socket of Jacob’s hip was dislocated while he wrestled with him. 26 Then he said, “Let me go, for the dawn is breaking.” But he said, “I will not let you go unless you bless me.” 27 So he said to him, “What is your name?” And he said, “Jacob.” 28 Then he said, “Your name shall no longer be Jacob, but Israel; for you have contended with God and with men, and have prevailed.” 29 And Jacob asked him and said, “Please tell me your name.” But he said, “Why is it that you ask my name?” And he blessed him there. 30 So Jacob named the place Peniel, for he said, “I have seen God face to face, yet my life has been spared.”
The man's name would not be revealed to Jacob. Which is interesting, the time had not yet arrived for that revelation.