What is the meaning of "cream of X" in a soup?

'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.

It is a specific process. After the soup is cooked, it is put through a blender. It is no longer chunks of food floating in a broth, but it becomes a homogenous creamy liquid.

Sometimes pieces of other food are added after the creaming to put some texture in again. Typical additions are croutons, swirls of sour cream, or minced herbs, all added at serving time. But you can also add fried bacon cubes, nuts, swirls of flavored oil, or whatever strikes your fancy.

update The comments insist that dairy cream is obligatory in a cream of X soup. This may be so in some culinary traditions. I grew up with "cream of X" soups which are defined by being a puree. They often, but not always, include dairy, and the dairy can be anything - cream, creme fraiche, a soft cheese, yogurt, or a combination. Besides, the homonyms "cream" as in "dairy cream made of milk" and "cream" as in "anything with a spreadable texture which I have a positive attitude towards" (like hand cream) are two separate words, and the soup is called "[spreadable-texture] cream of X", not "[dairy] cream of X". So it seems that there are cultural differences in the meaning.