I cry selective quotation.
Cambridge diction
Merriman-Webster dictionary.
Then, the all authoritative Urban Dictionary explaining point 2 in the Merriman-Webster definition.
Sprocket: a wheel with many cogs which interface with a roller chain.
Gear: A wheel with many cog which interfaces with another wheel with many cogs.
Cog replacement is a common engineering procedure where the broken cog (tooth) is removed, and a new one put in its place with the aid of a stud, a little bit like a dental procedure. If you walk into that engineering shop with your broken cogwheel (gear) and ask for a cog replacement, you 'll get one tooth replaced. If you ask for a gear replacement, they'll walk to the rack and give you an entirely new cogwheel.