A fixed aperture lens has just one aperture that is not adjustable. Fixed aperture lenses are very inexpensive to design and build.
Most are catadioptic lenses, like mirror lenses, and dirt cheap - long focal length prime lenses that have a fixed aperture, usually somewhere in the range of f/5.6 to f/11.
There are constant aperture zoom that list just their widest (maximum) aperture (usually f/2.8, or f/4), but can be stopped down to smaller apertures. Constant aperture zoom lenses are the most costly type of lens to design and build.
In the case of a constant aperture zoom lens set to it's max aperture, the aperture f-number value does not change as the lens is zoomed. However, the aperture size does indeed change as the lens is zoomed, but it retains the same focal length to lens opening size ratio which is what the f-number describes.
For example assume a 100 mm to 400 mm focal length, f/2 constant aperture zoom lens.
When the lens is set to 100 mm and f/2 the lens aperture at 100 mm is (f)100 mm/2 = 50 mm wide but the lens aperture at 400 mm is (f)400 mm/2 = 200 mm wide. As the lens was zoomed the aperture opening diameter got 4 times larger. So though it's called a constant aperture zoom lens, constant refers to the ratio of lens opening size to the focal length setting, not the actual diameter of the lens opening.
Variable aperture zoom lenses are in the middle as far as design and cost to build.
Using the same 100 mm to 400 mm focal length as above, but with an f/4 to f/8 variable aperture range, which says the maximum (widest) aperture at 100 mm is f/4, while the widest (maximum) aperture at 400 mm is f/8. Doing the math again we see that the lens aperture at 100 mm is (f)100 mm/4= 25 mm wide and the lens aperture at 400 mm is (f)400 mm/8=50mm wide.
The variable aperture lens opening only got 2 times bigger, because the focal length to lens opening size ratio did not remain constant as the lens was zoomed.
Note that we can calculate the lens opening size at any focal length between 100 mm and 400 mm if we know the f-number. Assuming the f-number ratio of the above 100 mm to 400 mm lens changes linearly, half way between 100 mm and 400 mm (at 250 mm) the f-number would be f/6. The math shows the lens opening diameter would be (f)250 mm/6=41.67 mm wide.
