Well, Marco, Mammillaria lanata is one of those names that is considered to be a redescription of another species, Mammillaria supertexta. It was described as having 12-14 white spreading radial spines, and no central spines! so your plants look a bit different!
Mammillaria supertexta was described as having 2 short (2-3mm) central spines, and 16-18 radials.
Spine counts are not a certain way of identifying species, merely a guide, but I woud suggest that neither of your plants are lanata or supertexta. I think that they are both forms of that much more widespread and variable species Mammillaria labilanata ssp. oaxacana.
I suspect that somewhere along the way, a nurseryman has got confused between the name "lanala" and the name "albilanata".