Most people conflate “Droid” with “Android,” but the two are not synonymous. Technically speaking, even The Droid Lawyer is misusing the Android and Droid names.
Android refers to the open-source mobile operating system owned by Google. Droid refers to the brand of smartphones exclusive to Verizon Wireless. (Check out this post for more terms.)
Verizon posted an infographic to clarify some of the confusion.