I guess the question is do you want to make it a Little Free Library, an Official Bookcrossing Zone (OBCZ) or both?
Little Free Libraries can be registered on the Little Free Library website, but I believe there's a fee for doing so. The LFL's location then appears on that website (which, by the way, is a totally different website and completely unrelated to Bookcrossing).http://littlefreelibrary.org/
To create an Official Bookcrossing Zone (OBCZ), all you need is the permission of the venue's owner/manager (in your case, that'd be you, as it's your house). You then let Support or the volunteeer region managers know here at Bookcrossing, and they can add the OBCZ logo to your OBCZ zone. Then you're off and running. No fee involved.
In terms of releasing books in a practical sense, there's a bit of overlap in that both Little Free Libraries and OBCZs provide an officially sanctioned place to leave and take books. Many Bookcrossers leave Bookcrossing registered books at LFLs with no issues.
The main difference seems to be in the actual physical make-up of the book exchange. It seems to me that Little Free Libraries tend to be sturdily-built, weatherproof, outdoor structures and OBCZs tend to mostly be indoor locations such as book shelves or book cases in publicly accessible buildings.