The gross morpho similarities between these two genera have been noted by others over the preceeding two decades.
The two genera are thought to be fairly closely related, but hard to believe that they are members of the Tricholomatacea with those odd spores! Both can show the vinaceious staining on the gills.
What are the color of spores in mass?
It is difficult to compare micrographs with SEM photos, but the spores linked to from the Asproinocybe page show rounded to elliptical heavily nodulose spores; spores in the genus Tricholosporum are starifome or knobbed cruciate spores. This appears to be a better spore match to what Alan shows us here.
Some species of Asproinocybe also have lactifers! These may not be present in Tricholosporum.
I will be curious to see the DNA work on these. What chimeric organisms they are!