TIME FOR OPINIONS AND INTERPRETAION! \o/ The way I see it (which is probably so far from the way you see it, but still!) is like this:
Genesis - They absorb the powers that to them are the powers of gods. Like getting hit by lightning. It's not enough to just witness it. You have to feel it, get caught by it, absorb the energy. Like drinking Artemis' vein, you allow it access into yourself, letting it adapt to you, and you to it.
Venari (I love that word, I fangasm'd a bit when I saw it. It's rare to see people play around with latin now'a'days) is more about understanding. This is probably the one I know of the best, since I always played a ranger in DnD, and when you had to get an animal companion, you don't just find an animal and say "You're my pet now!". You study it, understand it, learn to communicate with it on its own level. You allow yourself to dwell into a world you might not know about, so you can experience the ultimate bond; Understanding. Acceptance.
Stage three is a bit harder. You have understanding of powers beyond yours, while still knowing you braved the power. Like, if you stare into the eyes of death once, you will always carry that with you. You also have the power of friendship with you from Venari. So I guess I would go for something that reflects understanding of power, or something that reflects that sometimes you need support from a friend to be complete.
"Every friend you make adds another jigsaw piece to the puzzle that is [I]you[/I]."
Also holy god wall of text.
"To improve is to change. To perfect is to change often."