Is there a particular difference? The way they're overhauled is the same ? (I mean do we use the same overhauling methods ?)
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:
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.
The main difference is in how they operate, vs how they are maintained. Flow through a centrifugal compressor is turned perpendicular to the axis of rotation, while air in an axial compressor flows parallel to the axis of rotation.
Axial blades are airfoils that compress air by forcing it aft into a converging space via downwash the same as a wing generates lift by downwash. Efficient, but sensitive to angle of attack and aerodynamic stall, like a regular wing, so therefore sensitive to flow disruptions.
A centrifugal compressor is spinning duct that forces air into a converging space purely by centrifugal force imparted to air within it as it spins. Less efficient, but relatively insensitive to flow disruptions and way easier to make.