On www.quora.com, I got the request to answer this question:

Here’s my answer:
Focus breathing plus accepted tolerance. The focal length is defined when focused at infinity. Yet all lenses with internal focusing change their focal length while focusing. (Zoom lens are almost always internal focusing, otherwise, they would need an enormous helicoid and get very large.) You have to imagine a zoom lens has a moving group lens elements for zooming, another moving group of lens elements for focusing and yet another moving group of lens elements to compensate for the focus changes while zooming (so to keep it sharp while zooming). I don’t know if you ever had two girlfriends or whatever at the same time (or whether your girlfriend or whatever had two you’s at the same time), but you can imagine that it makes things complicated. Same in a zoom lens.

In short: This means that the focal length gets shorter when getting closer. In the case of a 70mm that might mean it’s effectively 65 or even 60mm up close. It’s mostly not a big deal, it’s just one of the many consequences of lens design, which is one big tradeoff. Now I don’t know which Sigmas you are referring to, but the 24-70mm f/2.8 ART suffers from some focus breathing at the long end. Several iterations of Sigma’s 70-200mm f/2.8 too as far as I remember, and then also on the long end. So if you set both lenses to 70 mm, one will suffer from focus breathing a lot more than the other, since in one case 70mm is the short end, in the other, it’s the long end.

Another fact of life is that focal lengths do have some tolerances. 70 mm even at infinity, is never exactly 70 mm. It will more likely to be something like 67,6 mm or 72,4 mm. If your lens suffers from focus breathing, this is one of the ways to compensate for it, but sometimes it’s just the way a lens design turns out. There are also ISO tolerances here, so don’t start to measure your lens and hope to get your money back. And really, those are general things, all manufacturers basically have to deal with the same optical limitations in lens designs and then make their own tradeoffs.

If you own the Sigma Art, you will probably also notice the 24-70 is less sharp in the corners at 70mm. So keep that in mind and change to the 70-200mm while making pictures if you need the focal length and/or sharpness.

One last remark: the fact that you use a D7500, so an APS-C camera with those lenses, doesn’t change anything, as long as you use the same camera with both lenses. The camera crops the image 1.5 x but in both cases.