IMHO, They are related but distinct terms though in some cases are used (almost) interchangeably.
Iris describes the adjustable mechanisim which controls the opening (aperature) of the focal tube, limiting the light delivered to the focal plane.
The term F-stop though can be used two different ways, and this is often the reason for confusion:
- In the photography world, f-stop can mean the points at which an aperture (iris) can be adjusted to. Each of the clicks or 'stops' is labeled with the f-stop value to which it corresponds.
- It can be shorthand for f-stop number, which in the general sense, means ratio of length to width of the focal tube.
Definition 1 is almost interchangeable with an iris, but you are using definition 2. So in your mind at least just think f-stop number, if it is referring to the ratio of length to width.
As the iris is closed the f-stop number increases.
Finally to be clear, as far as definition 1 one goes, an f-stop needs an iris to exist, since it refers to a mechanical adjustment to the iris itself. But in your case, definition 2, f-stop numbers exist regardless of whether an adjustable iris exists or not, since a focal tube does not need one.
Hopefully this was not more confusing. (Don't stare at the gif too long, it hyptnotizes.)