Millisecond pulsars may be formed by the accretion induced collapse of massive white dwarfs or from neutron stars spun-up by accretion from low-mass companions. Because the solid crust of a neutron star is expected to be moved by strong stresses which build up during spin-up or spin-down, the expected surface magnetic field structures are quite different for millisecond pulsars formed in these two different scenarios. During prolonged spin-up the moving crust compresses all stellar surface magnetic field into a small region around the spin axis. This can account for observed properties of disk population millisecond pulsars and their radio pulses, especially those of the most rapidly spinning ones such as PSR 1937+21 (two pulse components of comparable intensity 180-degrees apart; extremely narrow component widths; fan beam emission so that almost all such millisecond pulsars are observable despite the narrow widths; nearly 100% linear polarization and fixed polarization angle at radio frequencies below one GHz for one of the two pulse components). Radio pulse properties of typical millisecond pulsars in globular clusters appear to be different from those of the disk population, and may indicate a different genesis, e.g., accretion induced collapse, for most of these pulsars.