[agurk]

A pump moves a fluid and a compressor reduces the volume of a fluid. If your fluid is compressible, such as air, then moving it will entail some compression. This was the GP's point about a fan.

This means there are not two distinct binary categories of pump or compressor that these things can be neatly classified as. This is compounded a little as fluids are often erroneously thought of as only incompressible fluids like water without realising it's a much bigger category.

Due to my brainfart regarding turbines, I assumed the GP had misunderstood the mechanism of action so I used the simpler word pump to explain. It is not incorrect to describe the action of a turbocharger as pumping more air into the cylinder, especially in my native dialect of English.