These terms can be confusing. The old wording was different (as Clark commented). Maybe this is already clear from what 44-Henry posted above, but just to make it really clear, 18th-19th c. "cast steel" (as a compound word), is not the same as 20th c. and later "cast steel" (verb plus noun, where melted steel is poured as liquid into a mold).
The 18th-19th c. version is just another name for crucible steel. The alloy components were melted in a crucible to make steel. The ingots were then forged or rolled (to make sheet steel for saws, plane blades, clock springs).
So when you buy an antique Sheffield backsaw stamped "cast steel", it doesn't mean that metal was melted and pouring into a mold in the shape of a saw. It just tells you what type of steel was used. As Clint said, 18th-19th c. cast steel was just a raw material. As I understand it, the big advantage was in consistency (even mix) throughout the product.
Here's a brief description I found yesterday (from
https://www.thoughtco.com/steel-history-2340172 ):
One of the earliest forms of steel, blister steel, began production in Germany and England in the 17th century and was produced by increasing the carbon content in molten pig iron using a process known as cementation. In this process, bars of wrought iron were layered with powdered charcoal in stone boxes and heated.
After about a week, the iron would absorb the carbon in the charcoal. Repeated heating would distribute carbon more evenly and the result, after cooling, was blister steel. The higher carbon content made blister steel much more workable than pig iron, allowing it to be pressed or rolled.
Blister steel production advanced in the 1740s when English clockmaker Benjamin Huntsman while trying to develop high-quality steel for his clock springs, found that the metal could be melted in clay crucibles and refined with a special flux to remove slag that the cementation process left behind. The result was a crucible, or cast, steel. But due to the cost of production, both blister and cast steel were only ever used in specialty applications.