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Here is the small $12 \; V$ pump that I am looking at. The manufacturer called the product as DC brushless centrifugal circulation small water pump but under its description it mentions that it is a single stage pump.
I wonder what the difference is? Is it a misleading description or title or do those terms are used interchangeably?
Single stage and centrifugal are describing two different properties.
A single stage pump is a pump that only has one acting impeller stage doing work on the fluid. If you put two pumps in series, you could say that you have a two-stage pumping setup. Some pumps are built with multiple stages - this is usually for high pressure applications.
A centrifugal pump is the style of impeller / casing. Centrifugal pumps use an impeller similar to what is shown below, and they rotate in a way that utilizes centrifugal force to do work on the fluid, in this case creating pressure and driving the flow.
You could have a single stage centrifugal pump, a multiple stage centrifugal pump, a single stage NON-centrifugal pump, or a multistage NON-centrifugal pump setup. Below is a generic example of a multiple stage centrifugal pump - note that there are multiple impellers, and they don't have to be completely separate pumps - each of these increases the pressure supplied to the next impeller, so as to increase the pressure of the next impeller's discharge.
For the vast majority of applications (especially water), single stage centrifugal pumps sized correctly cover most applications.
