A teacup is traditionally 6 fluid ounces while a measuring cup is 8 fluid ouncs, in the United States of America. Europe and Asia may differ. Japanese tea cups are about 3 fluid ounces.
Generally, there are 6 ounces in a teacup. One cup is 8 ounces, so a teacup contains less cups than a measuring cup. Usually, measuring cups are bigger than just one cup.