The pupping and wool seem off for that Mammillaria. It reminds of something I have as M. standleyi, but that one does not make that many offsets, but this kind of offsetting can be a mutation.
May I suggest that the poster tries and makes sure that what the label on the plant says is correct before sticking things in the Database? Google is not great but usually comes up with enough true to type images to determine if a plant is not what it is labeled at.
