Although not often, they can both exhibit hexagonal and pyramidal shapes.
Both are abundant on Earth.
Differences between calcite and quartz
The property of hardness: Calcite is much less harder than quartz, while the latter is over three times harder than calcite.
Their chemical composition: Although they are both minerals, their chemical composition significantly differs. Calcite is made from calcium carbonate while quartz is made from silicon dioxide.
Their shape: The shape is one of the easiest way to identify minerals as you normally don't need to perform an experiment as the case of chemical composition differences. Quartz minerals usually exhibit hexagonal shapes while calcite minerals usually exhibit rhombohedron shapes.
