A.A. Milne, author of the "Winnie the Pooh" series, wrote an entire comic essay based on the notion that he had "not yet discovered, in spite of recent familiarity with house-agents (real estate agents), the difference between a fixture and a fitting." Indeed, the paper-thin difference between the two has led to legal disputes between residents and their insurers, as well as buyers and sellers of real estate.
A fixture is defined as something that has been at least "securely" and maybe even "permanently" attached to a house. Chandeliers, kitchen sinks and dishwashers could all be examples of this. Bookshelves that you have to screw into a wall are commonly defined as permanent fixtures in lease agreements.
Depending on which definition you read, "fixture" is listed as part of the definition of "fitting" or as an item considered a supply or part. In a house, this could be a shower head or a new set of pulls for your cabinets.
Renters often run into controversy when they install new fittings and find out that they have become fixtures. Installing your own shower head, or adding your own kitchen shelves can get you into a tricky situation, because those can be considered "securely attached" to the dwelling, and generally fixtures stay with the property when you leave.
If you are a renter, get permission from your landlord before installing anything new that might be construed as a "fixture" when you move out. If you are selling your house and want to take some of the "fittings" with you, add these items to the seller's disclosure form so that potential buyers have no misunderstandings.