Well, in Connecticut: "a person commits "home invasion" by entering or remaining unlawfully in an occupied home, with the intent to commit a crime."
Citation from Connecticut statute?
Irrespective of statutory language, in common parlance a "home invasion" is what occurs when a person or persons break into a house with the intention of taking the occupants hostage and either robbing the, beating them up, and/or killing them. In commonly accepted use, a burglar sneaking into your house and lifting the silver from the dining room sideboard while you sleep through it upstairs would be considered a "hot" burglary, but not a "home invasion."
Which is why, early in this thread, I commented that if you are involved in a home invasion (as the victim), you won't have to go looking for the invaders because they'll be all over you like bees on clover.