"Is a Centrino the same as a pentium M processor? " - click here&
"Centrino Processors: Say a 1.4Gig Centrino processor costs four or five times at least as a 1.4 desktop processor does. Is the 1.4 centrino processor only as fast as a 1.4 gig desk i.e. athlon/intel processor? Are the extra costs all to do with the extra architecture which makes it so economical with battery life?" Errr I think it is because it has 1MB of Cache.
"If I got one, would it struggle to run 3d games, or does the extra architecture on the chip ensure that it works fine?" - Would depend upon the graphics card and RAM - I can play games on my laptop fine...But you cannot beat a desktop.
"With these processors, is there a speedstep built in as well, so that when a power source is removed e.g. mains, it switches to a slower speed?" - Yes.