There is no "mistake", it is the accepted terminology, in the United States marketplace. The terminology does not describe the design principle of the pump and nobody seems to be confused.
There are many intelligent pump experts that use the terminology so it does not cause my nose to get out of joint:
Igor Karrasik's as well as the Hydraulic Institute's definition of a centrifugal pump:
"A centrifugal pump is a simple machine consisting of a set of rotating vanes enclosed within a housing or casing."
"An axial flow pump is essentially a high capacity low head centrifugal pump."
per A.J. Stepanoff's "Centrifugal and Axial Flow Pumps":
"Centrifugal pumps comprise a very wide class of pumps in which pumping of liquids or generation of pressure is effected by a rotary motion of one or several impellers. In the early stage of centrifugal pump development, pumping was ascribed to centrifugal forces. Later this class of pumps was extended to include axial flow pumps, and the conception of the centrifugal action of the impeller was inadequate to explain the operation of axial flow pumps. However, treatment of axial flow pumps as a class by themselves was not justified, because hydraulically they represent one extreme of a continuous series of pump types. This continuity applies to both theoretical treatment and design methods. Some intermediate types are called mixed-flow pumps. In these, the flow through the impeller has both radial and axial components and the impeller resembles a ship propeller."
Per "Pumping Station Design" by Garr Jones:
"In colloquial usage in the United States, a "centrifugal pump" is any pump, in which the fluid is energized by a rotating impeller whether the flow is radial, axial, or both (mixed)"