I just printed this quote from Amadaeus Grabau in the Dry Dredgers bulletin this past month. It is in agreement with answers of others but this old time quote is a good one:
Solution and the Formation of Molds and Casts (p.100) – Amadeus Grabau 1899
“Carbonated, or otherwise acidulated waters will dissolve calcareous fossils, if the strata in which they are embedded are pervious to the water. Thus, a mold of the exterior of a dissolved shell, for example, may remain in the rock, while a mold of the interior, formed by the mud or sand which found its way between the valves, will remain within the mold of the exterior. If the rock is under pressure, it may happen that the two molds are pressed against each other, and the stronger features of one may become superimposed upon the weaker features of the other. Thus, fossil mussels may show the external striæ impressed on the internal mold, showing at the same time the muscular impressions in relief. Occasionally the space between the two molds, i.e. that formerly occupied by the shell, may be filled by infiltrations, and a cast of the original shell may thus be produced.”
I believe the key to remember here is that a mold is made from an original object (or facsimile thereof) while a cast is made from a mold. A cast reproduces the actual original object in form. So, your footprint in mud is a mold of your foot. Plaster poured into that mold makes a cast reproduction of your foot.