So what is the difference between a tea cup, a coffee cup, and a chocolate cup? Mostly it is the shape.
Tea cups have a wide open rim that tapers down to a small base and the handles are designed to hook a single finger. Porcelain is a great conductor of heat. So it is the perfect material for boiling water and tea leaves. Tea cups were designed to coll quickly and not burn the fingers of the tea drinkers. They average 4-6 ounces.
High tea, by the way, is a supper or meal served in the late afternoon or early evening. It was served at a high table or regular dinner table. Low tea is the fancy tea served from about two to four o'clock in the afternoon in the parlor. It was served on low tables or tea tables and was considered a snack to tide you over until a late dinner around eight or nine o'clock.
Coffee cups have a more vertical side and a bigger handle for two or three fingers. Coffee is usually not brewed at such a high temp., it is brewed around 180 F. Burning your fingers and your tongue is not such a risk. Also, the vertical shape helps settle the sediment or grounds. Coffee cups with a saucer average 4-6 ounces.
Modern coffee cups with saucers often have a tea cup shape, but this is a relatively new design, dating from the mid-twentieth century. I think of them as dinner cups or cups used on trains or in diners. Dinner cups were a commercial shape for restaurants, and were not used in homes until the 1940's or 1950's.
Mugs are a whole new story.
Chocolate cups have a narrow vertical shape. They are smaller and around 4 ounces. Chocolate in the 1800's was served as syrup made of sugar, water, and cocoa. Milk or cream was then carefully poured on top. So the shape of the chocolate cups kept the milk or cream from cooking or curdling. The drinker sipped the chocolate syrup through the cream to enjoy their drink. We do the same sort of thing with our hot chocolate and whipped cream.
More than you wanted to know? Get me started on casseroles versus tureens. Or do you know what a celery dish looks like? Ok, ok. Another day.