Two issues at play here, rounding and breathing.
The specified focal length is usually rounded slightly, usually not by much. I don't know the exact values, but for example the 70-300L might be 71.9 - 296.8 mm. This usually isn't a big enough difference to notice.
Breathing is the change in apparent focal length with focusing distance (distance to subject). The actual (and specified) focal length(s) are with the lens focused at infinity. As you focus closer, the 'apparent' FL gets shorter. For the 70-300L, that decrease in apparent FL is greater than many lenses, due to the design. Many zoom lenses lose a significant amount of their sharpness when they are focused near or at the minimum focus distance (MFD). The 70-300L does not, because Canon used a floating focus system in the lens. However, if you look at the specs for the lens, you see that it has the same MFD and maximum magnification value of the 70-200/2.8L IS II. That means that while the 70-300L is 300mm at the infinity focus point, by the MFD it is giving you the FoV of a 200 mm lens.
Did you try comparing the lenses in question with both of them focused at infinity?