An "Easter egg" is a hidden message or an in-joke in a TV program, book, computer program, video game, movie, etc.
A "rabbit hole" is a portal to another world in a in a TV program, book, computer program, video game, movie, etc. In an ARG a rabbit hole is the site or events that lead into the game world.
Both Easter eggs and rabbit holes can be part of designing an entertainment experience that rewards true fans.
For example, as discussed in a Nov. 23rd. 2011 Huffington Post blogpost , an NBC show recently included an "Easter egg" that only the most devoted fans of Community and pop culture would appreciate. Watch the video below to see how Beetlejuice, a bizarro character in black and white stripes, is summoned from the grave by characters on NBC's Community who (over the course of 3 seasons) say Beetlejuice's name three times and, according to the storyworld of that the 1988 horror-comedy film, release the obnoxious and perverse clown (opening up a rabbit hole from one storyworld into another?).