Crop factor

The same head size on a smaller sensor needs a shorter lens, and that changes the blur.

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Same framing, different sensor

This page opens a 56mm on APS-C beside an 85mm on full frame. Both keep the subject the same size, so the APS-C camera stands closer. The field of view is similar. The background blur is not, because the focal lengths and the sensor sizes differ. Open the aperture presets, or match depth of field, to see what f-number the full-frame side needs for the same blur.

A DSLR and a mirrorless camera with the same sensor agree. The mirror does not change the crop. Medium format goes the other way: a longer lens, or a larger sensor at a similar focal length, blurs the background more easily. The format comparisons are listed under lens comparisons.

Questions

Is APS-C just a crop of the full-frame picture?

Only if you use the same lens and stand in the same place. For the same head size you fit a shorter lens and stand closer, so perspective and blur both change.

What does 56mm on APS-C stand in for?

About 85mm on full frame, for framing. The page shows that pair. The blur still differs until the apertures are matched for depth of field.

Why does medium format blur more easily?

The larger sensor reaches the same background blur at a slower f-number. An 80mm on medium format beside an 85mm on full frame is the comparison for that.