I hate to disagree with Ilife, but Opuntia rufida is a completely different plant not at all related to Opuntia microdasys, which is correctly mentioned lower down on the web page Jai linked to as being the major species this plant is related to. Opuntia rufida is a large bushy cactus occurring among other places in southwestern Texas, where it occurs in two distinct habits that are associated with the glochids on the pads being recessed or protruded, which is confusing enough in itself for this little guy to be thrown in the discussion.
The version with the recessed glochids is a very interesting plant to grow and could possibly be a mutated version of Opuntia rufida, but it occurs quite expansively in the wild.
I think that the correct name for this mini Opuntia is Opuntia microdasys var. rufida f. minima. Opuntia microdasys var. rufida is a form of Opuntia microdasys with red-reddish glochids, which tends to get slightly larger pads and sometimes size than regular Opuntia microdasys and because of that can become confused with the form of Opuntia rufida that has protruding red glochids. So that is where the confusion with O. rufida comes from.
Given that this is a dwarf version of the plant you'd add the 'forma minima' to indicate it is not the regular sized plant. I had this plant for quite a while and as Hamwild already mentions it stays small, before it eventually succumbed to the harsh summer conditions here. Regular prickly pears have a hard time here, so mini versions have it even harder.
