Abrasive Discs
Abrasive discs are mainly used in metalworking and exist in several varieties. For example, they may be suited for grinding or cutting, consist of sandpaper or resin-embedded abrasive particles, and are optimized for different materials.
Cut-Off Wheels
Cut-off wheels come in a wide range of sizes and may fit on a rotary tool, disc grinder or even a chop saw.
In order to cut effectively, these discs are very thin. They should not be used for grinding (workpiece contacting the faces) as that could cause them to shatter!
Grinding Discs
Grinding discs are thicker and sturdier than cut-off wheels which makes them suitable for grinding ("sideways" material removal). You should not attempt a cut with these discs, they have a much too large contact area then and will overheat and cause strong kickback.
These discs are usually made for disc grinders.