What is the difference between a cough drop and a lozenge?

The are the same:

"A throat lozenge or cough drop is a small, medicated candy intended to be dissolved slowly in the mouth to lubricate and soothe irritated tissues of the throat (usually due to a sore throat), possibly from the common cold or influenza. Cough tablets have taken the name lozenge, based on their original shape."

https://en.wikipedia.org/wiki/Cough_drop