What is the meaning of "cream of X" in a soup? I have often had "cream of tomato" or "cream of mushroom" soup. But I still have no idea how the recipe or preparation differs from "normal" soup.

What is the difference? Is it a specific ingredient or a specific process? I tried a few searches online, but they all show recipes instead of an answer.
'Cream of' originally meant not only pureed, but cream added, regardless of other ingredients - most modern shop bought versions will either have cream or a product of dairy origin added, which is why there are often warnings about lactose intolerance on 'cream of' soups.