Plaque is a biofilm:
Plaque is the collection of bacteria that can build-up on teeth within minutes. The bacteria gather together and form a complex network called a biofilm. You can probably feel plaque on your teeth if you forget to brush in the morning. Fortunately, routine brushing and flossing can remove plaque fairly easily.
Calculus is hardened plaque:
Calculus is plaque that stays on your teeth for a long enough period of time to become hardened with minerals. This is what you may have felt being removed during part of your routine dental cleaning. Calculus removal is one of the most important reasons to come to your routine cleanings because it cannot be removed with a toothbrush or floss. The buildup of calculus over time can cause severe issues such as inflammation and gum disease.