Re: Why does my 24-105 have a different magnification ... ?

If I may take the numbers Bill already provided and give a "physicist" explanation with a couple of formulas.

For a thin lens, the distance between the object and its image is given by:

(2+m+1/m) * f = object-image distance ala MFD

where m is the magnification and f is the actual focal distance measured at MFD. This formula works exactly only when the two principal planes of the lens coincide (the blue H and the red H' in Bill's diagrams). For neither of these two lenses the two planes coincide. In fact, for one lens the blue H goes in front of the red H' and for the other lens it is the other way round. This mismatch, the distance between these two planes, is called hiatus and it can be included in the above formula, so it works again:

(2+m+1/m) * f = MFD - hiatus

Let's plug the numbers in:

Panasonic: (2+0.5+2) * 73.3 = 298.2 + 31.7 = 329.9 mm

Sigma Macro: (2+1+1) * 75.7 = 312.4 - 9.7 = 302.7 mm

All checks out.

So, yes, there is focus breathing for both lenses and neither lens is 105 mm at close focus, but the difference between the two lenses is very small: 73.3 mm vs 75.7 mm. What makes the difference for the magnification is the hiatus: the negative hiatus for the Panasonic zoom makes the effective path the light rays travel 31.7 mm longer but the effect is opposite for the Sigma.

The bottom line is that the MFD alone does not define magnification. You need to know both the actual focal length at the MFD and lens hiatus.