Black-footed Albatross, off Newport, Oregon, 15 May 2011 by Greg Gillson.
The wing of birds is analogous to the arm of humans. This is most evident on longer-winged birds like the albatross above. They have a shoulder, elbow, and wrist. They have similar bones--a humerus in the upper arm, and radius and ulna in the lower arm. The hand, or manus, is composed of several fused hand and finger bones--it's more like one long finger.
Primaries are attached to the hand. Primaries are numbered from inner to outer, P1 to P10 in the photo above. Birds have from 8-11 primaries, depending upon species. In general, most non-Passerines have 10 primaries; most Passerines have 9 primaries.
Secondaries are attached to the ulna. Secondaries are numbered from outer to inner. Birds have a variable number of secondaries depending upon the length of the wing.
Primaries and secondaries are called the flight feathers of the wing, or remiges. (The tail with its retrices, are also considered "flight feathers.")
True tertials or tertiaries are feathers attached to the humerus, the bone from shoulder to elbow. They are not considered to be flight feathers, or remiges. Very long-winged birds have more tertials than shorter winged birds. Some bird families, including shorebirds and gulls, have modified tertials that are longer and distinctively marked.
In many smaller birds the humerus is so short as to be lacking separate tertial feathers. However, sometimes the inner 3 secondary feathers on passerines are called tertials when differently shaped or colored than the other secondary feathers.
Black-footed Albatrosses have 10 primaries, 25-29 secondaries, and numerous tertiaries or tertials.
Western Gull, Beaverton, Oregon, 17 February 2009 by Greg Gillson.
Most gulls have 10 primaries and 24 secondaries. They also have some true tertial feathers.
Vaux's Swift, Forest Grove, Oregon, 22 September 2009 by Greg Gillson.
Vaux's Swifts have 10 primaries, but only 6 (or 8, if you count very tiny) secondaries.
The very different lengths of the parts of the arm cause different styles of flapping.