Actually the opposite is true. The sample sizes for discrete data are always larger than continuous. Think of this example, if a child seems sick, a parent will need more information to confirm if they are truly sick. Sick or not sick is discrete data. The next question is usually, “What is their temperature?” which is request for continuous data. If the temperature is 99 degrees Fahrenheit then the child is probably fine, but if the temperature is 104 degrees Fahrenheit then the child is very sick and needs to go to the hospital. Only one point of continuous data provides enough information to make a decision.
I hope that helps. If you try any online sample size calculators you’ll find the sample sizes to be very different. Continuous is always smaller.