A measuring cup is a specific size, about 237mL. There’s a whole system of US measurements, actually:

3 teaspoons in a tablespoon

2 tablespoons in an ounce

8 ounces in a cup

2 cups in a pint

2 pints in a quart

4 quarts in a gallon

Not all cups are measuring cups; if you are having a cup of coffee that doesn’t mean your cup is exactly 8oz. You just infer from context that if someone is talking about ingredients then you should measure them with a measuring cup.