Di lenses are lenses design for film and digital camera. but with a coating meant to reduce reflection from sensor, same as Sigma DG. http://www.tamron.com/lenses/prod/di.asp
Dii lenses are lenses design for Digital camera with APS size sensor, thus they cannot be use on film camera or any digital camera with sensor larger than APS size http://www.tamron.com/lenses/prod/diII.asp
Di:
Designed for use with both 35mm film SLR and digital cameras.
Di lenses are designed to fit the characteristics of digital cameras as well as film cameras by incorporating countermeasures against ghosting and flare through such advances as special coatings.
Di II:
Designed for exclusive use on digital cameras with smaller-size imagers.
Di-II lenses are designed exclusively for digital SLRs with smaller-size imagers.
This series of lenses is not designed for 35mm film format cameras and digital SLR cameras with image sensors larger than 24 x 16mm.