What is the difference between axial compressor blades and centrifugal compressor blades?
The blades are shaped completely differently. Typically a centrifugal compressor is one solid piece that looks like a turbocharger and an axial compressor is a flat disk that looks like a fan with individually manufactured blades inserted, though axial compressor disks with integral blades "blisk" is starting to be used. Here are compressor pics that show how they are used:

Two stage radial/centrifugal compressor circled (with a three stage axial turbine following)


Fifteen stage axial compressor


A radial compressor can usually generate higher pressure in a single stage so it's usually simpler, while an axial compressor is easier to stack in multiple stages to get much higher pressure ratios.