Final answer:
A rate is a comparison of two different quantities with different units, while a unit rate simplifies that comparison to the amount per one unit of the second measurement. Rates can involve any amount, but unit rates refer to the ratio per single unit.
Step-by-step explanation:
The difference between a rate and a unit rate lies in how each one presents information. A rate is a comparison of two different quantities that have different units. For example, if you drive 150 miles in 3 hours, the rate of your driving is 50 miles per hour (mph). This is calculated by dividing the distance (150 miles) by the time (3 hours).
A unit rate is a specific type of rate in which the denominator is 1. Using the previous example, the unit rate of driving would be 50 miles per 1 hour, or simply 50 mph. It's a way to express how much of something occurs or exists in a single unit of another thing. In essence, the unit rate gives you a direct measurement of the ratio per one unit of the second measurement.
An example in another context might be a person's wage. If you earn $120 in 4 hours, that would be a rate. To express it as a unit rate, you'd convert it to how much money you make per hour, which would be $30 per hour ($120/4 hours).