This may offend some purists out there, but the answer is: effectively nothing.
When people use the terms differently, it’s often to distinguish between the size and scope of cleaning. In this case, janitorial services refers to the basic cleaning (dusting, trash service, restroom cleaning, mopping, and vacuuming) of a smaller facility. Commercial cleaning then refers to things like scrubbing tile, stripping/waxing floors, carpet cleaning, window cleaning, etc. in a larger facility.
However, there is so much overlap between these services (and so many companies that do all of them) that this distinction isn’t usually very helpful. Use whichever one you like, and you will probably always be understood.
For our part, we use the terms nearly interchangeably on this website. When we describe our own work as commercial cleaning, it’s just to make sure that we’re communicating the scope of our work.