The parts of a light fixture, named

A light fixture has about eight parts, nearly all of them buyable separately for a few dollars, and the only thing standing between a broken lamp and a working one is usually knowing what the broken bit is called. "The metal bit that holds the shade" returns nothing useful. "9 inch lamp harp" returns the exact part.

This page is the vocabulary, split into the two cases that matter: a fixture mounted to a ceiling, and a lamp that stands on the floor or a table. They share more parts than people expect.

Every hardwired fixture hangs off the same four inches of hardware, whatever it looks like below that.

A lamp is the same idea turned upside down, with one extra system - the shade support - that ceiling fixtures mostly do not have.

The fitter is the part that catches people out. There are three systems and they do not interchange. A spider fitter sits on a harp and is held by a finial - the common one. An uno fitter threads directly onto the socket collar and needs no harp at all. A clip-on grips the bulb itself. Buying a shade without checking which one your lamp uses is the single most common lamp-parts mistake, and it is solvable with an adapter rather than a return.

A spare socket: the DiCUNO UL Listed 3-way socket. The part that actually fails. UL Listed, which much of this category is not, and 3-way so a lamp keeps its low-medium-high after the repair.
Who should skip it: anyone whose lamp was never 3-way and never will be - the plain on/off version is cheaper and simpler.

A harp in the standard size: the 9 in. harp set with a 3/8 in. saddle. 9 inches is the commonest table-lamp harp height and 3/8 in. is the standard saddle, so this fits more lamps than any other single size. A finial is in the box.
Who should skip it: anyone whose lamp uses an uno fitter - there is no harp on those at all.

Spare finials: the Creative Hobbies ELY505 brass finial. The part most likely to be missing from a second-hand lamp, and the reason its shade sits crooked. Solid brass, 1 in. tall, two per pack.
Who should skip it: anyone with nickel or black lamp hardware - brass will not match.

The adapter that rescues a wrong shade: the threaded uno bridge adapter. Bridges a spider shade onto an uno lamp, which is the mismatch people discover after the shade has arrived.
Who should skip it: anyone with a slip uno rather than a threaded uno - they are different, and this is the threaded one.

Sizing a shade or a harp is its own set of measurements - lamp shade, harp and fitter sizes has the charts.

Naming the bulb rather than the fixture - bulb shapes and bases explained does for A19, BR30, E12 and E26 what this page does for canopies and harps.

Taking a hardwired fixture off the ceiling and plugging it in instead - converting a hardwired fixture to plug-in is the renter route.