Difference between rate of elimination and clearance?
Clearance is a measure of the volume of plasma from which something is removed, per unit time. For instance, it could be 2 mL/min, meaning that every minute, a two-milliliter of drug plasma is cleared. In other words, it is the rate of drug elimination divided by the plasma concentration.

Remember that the elimination rate is in units of inverse time, so dividing it by inverse volume gets you volume over time, which is the standard dimensionality of clearance.