We moved into a home with a suited bathroom on one side of the basement wall at floor level and a bathroom on the unfinished side of the basement on the other side of the same wall that has the toilet and sink on a platform about a foot above the cement floor. Why is this and how can the second toilet be plumbed to sit on the floor?

Sounds like something that a home owner did himself but didn't know how or didn't want to cut the basement floor.

A good guess (without being there to peer under the raised platform) is that the concrete was poured with plumbing in it for one bath, and the raised one was added later by someone who didn't want to jackhammer the concrete.

My guess too!