As my grammar book (Korean Grammar in Use) explains it, "지금" means "now" as referring to the current moment. "이제" means "now" with a sense of separation from the past. You can think of "지금" as meaning "right now" and "이제" as meaning "from now."
"지금" would be the "now" in "I'm sorry, but she's busy now."
"이제" would be the "now" in "I know better now."
At least, that's my understanding of it as a non-native speaker.