Plaque is a soft, sticky, colourless (when build up becomes abundant it can appear white) film containing millions of bacteria and is constantly forming on the surfaces of your teeth. Due to plaque accumulation being a constant cycle within the oral cavity, brushing and flossing 2x a day is extremely important in order to disrupt the bacterial formation/growth. If plaque is not removed regularly from the surfaces of the teeth the bacteria continues to grow causing the gingiva (gums) to become red, swollen, and eventually start to bleed. When the gingiva is in this state it is also known as gingivitis.
Calculus also known as tartar is a hard, smooth build up on the tooth that appears yellow in colour. Calculus formation occurs over time from the exposure of minerals in your saliva that calcify or harden plaque. Essentially calculus is old plaque that can no longer be removed by tooth brushing or flossing and can only be removed by a dental professional.