An f-stop is a relative aperture, and the 'relative' part takes the focal length of the lens into account - so f/2.8 on a 28 mm lens results in effectively the same illumination at the centre of the film plane as f/2.8 on a 280 mm lens, apart from any difference caused by transmission losses in the lens.
The transmission aperture (T-stop or T-number) takes the losses in the lens into account: reflections at air-glass surfaces mostly. The T-number is the f-number of a lens with 100% transmittance that would give the same on-axis illumination for an object at infinity. The difference between the f-number and T-number is nothing to do with the focal length of the lens, it is more to do with the number of elements in the lens and the efficiency of the coating etc. Most modern lenses have something between a quarter and a half a stop difference between the f-number and the T-number, which is pretty insignificant. Older lenses, especially zoom lenses with many elements, may have up to a stop difference.
As an aside, f-numbers are used for focus calculations, whether or not T-numbers are used for exposure, because f-numbers are geometrical.
The effect of an adapter (converter) depends on the adapter, and where it is. A wide angle adapter is almost always in front of the lens (Tele adapters can go behind or in front of the lens). The f-number of the lens is the focal length divided by the diameter of the entrance pupil (the image of the lens iris when seen from in front of the lens). When you put a converter in front of the lens both the focal length and the diameter of the entrance pupil change, and they pretty much change in proportion (this is a simplified version of the whole story, maybe this thread will evolve into something more rigorous). This means that the f-number doesn't change significantly (this is an advantage of teleconverters that go in front of the lens - the downside is that they have to be physically large enough to maintain the new size of the entrance pupil). The important concept is that the f-number is not calculated from the physical diameter of the iris, but the apparent diameter*, and the apparent diameter can change.
When you put a converter behind the lens things are different. The focal length changes, but the diameter of the entrance pupil doesn't. Therefore the apertures marked on the lens are no longer correct, so they need to be offset. Once again, this isn't the full story because the exit pupil diameter has changed, and that has some bearing on the issue.
I'll just reiterate that this isn't a rigorous explanation, but I hope that it is OK to begin with, especially in conjunction with the other good replies you will get here.
Best,
Helen
*There is a special case where the iris is in front of the lens elements. In this case the entrance pupil and the iris are the same.