When we say a light source emits 1500 lumens of light, it does not really matter if the light source is incandescent, CFL, diode etc. Similarly, when I say f/1.8 can I assume that all lenses pass the same amount of light at that f stop? If I am incorrect in this, is there a term that tells me across all lenses the amount of light they will pass through to the sensor?
No, this is not the case. Aperture F stops are calculated on pupil size and focal length of the lens.
Whereas a T-Stop is a measured unit and lenses set at the same T-Stops will make the same exposure.
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Basically, yes. From an optical perspective assuming you compose the shots similarly then different lenses with the same f/number will produce the same exposure. This is why the f/number is specified instead of the entrance pupil size (which is focal length divided by f-number).
To expand on this last point lets say we have a 100mm lens which has an entrance pupil of diameter 50mm. This means the maximum aperture opening appears to be 50mm wide when viewed from the front (the actual hole in the lens will be slightly smaller, as it is magnified by the lens elements, however this is not optically relevant - appearance is what matters).
Let's say we also have a 200mm lens which also has an entrance pupil of diameter 50mm. It would be tempting to thing that because both lens openings (apertures) are of equivalent size then these two lenses would produce the same exposure when photographing a uniformly illuminated white wall.
However the wider field of view 100mm lens views more of the wall (4 times more in fact) then the 200mm lens, whilst at the same time projecting the same image circle onto the sensor. 4 times more wall means 4 times more light onto the sensor, which equates to two stops difference in exposure. To get the same exposure we'd need an opening with 4x the area, i.e. double the diameter: 100mm.
It would be really convenient to have some value to quote for lenses that took this into account so you could know when exposure to expect from the lens. We've seen that a doubling of focal length requires a doubling of entrance pupil diameter to maintain exposure, so it's the ratio of these two values that determines exposure. Thus we can divide the focal length f by the entrance pupil diameter to create our new exposure determining value. Finally, to remind people of the meaning of this value we'll stick "f/" in front of it!
Thus our two lenses with equal size entrance pupils are actually f/2 and f/4!
This is all from an optical perspective, to address points raised in camflan's answer, in reality you might not get exactly the same exposure, due to different light transmission through the glass (a lens with the same f-number but different number of glass elements will absorb a different amount of light leading to a different exposure). The T-stop is a measure of how much light is actually transmitted, a throwback to when precise exposure matching was required when recording moving pictures on film.
However if you're going into this much detail then you also need to take into account the fact that the f/stop and t/stop numbers (as well as the focal length) are rounded arbitrarily by the manufacture anyway so there's no way to exactly predict exposure.
But two lenses with the same f-number will get you close enough for all practical purposes.