MTD owns Cub, Bolens, Troy Built, White, Yard Man, Yard Machines, and Ryobi brands of yard equipment. (they may own more, but those are what I am aware of).
There is SOME cross engineering of SOME product lines. Cub is their premium line and seems to be unique. Troy Built also seems to be unique.
Currently, there are no riding lawnmowers in the Cub or White brands being offered. Sears Craftsman has one riding mower, it used to be marketed by Cub, it was later switched to White, and is now not sold under either of those brands. It may or may not be available under some other brand names of MTD. Sears sells this unit under the Craftsman brand name.
Toro currently does not offer a riding lawnmower, however they do offer some small residential ZTRs.
I found 2 small units on the Deere website, but I have been told they are discontinued or will be discontinued. I don't know if that is true or not.
Snapper has 3 riders available, each is available in a couple variations.
Don't have a clue about Simplicity.
I believe Murray makes a couple units, they sell them under various brand names. I've seen them at Sears and at a couple box stores. I'm pretty sure they are Murray, might be American Yard Products (in fact they might be the same company???).