I seem to recall the 10" rolls being for aerial-cameras, or was that 9 1/2" ?? I used to print the stuff a quarter of a century ago and I can't remember! It would be either aerial-camera or one of the banquet-camera formats.
The base refers to the thickness. 135 is slightly thicker than the usual rollfilm 120 thickness and might slightly affect loading (reduced capacity) for a roll-core or film-magazine.