  To track the formation and evolution links of the millisecond pulsars (MSPs)
powered by accretion and rotation in the Galactic field, we investigate the
spin period (P) and spin-down power (Edot) distributions of the MSPs observed
at the wavebands of radio, X-ray, and {\gamma}-ray. We find that all but one
(119/120) of the {\gamma}-ray MSPs have been detected with the radio signals
(radio+{\gamma} MSPs); on the contrary, nearly half of the radio MSPs (118/237)
have not been detected with {\gamma}-rays (radio-only MSPs). In addition, the
radio+{\gamma} MSPs are shown to be the relative faster and more energetic
objects (<P> ~ 3.28 ms and <Edot> ~ 4.5 * 10^34 erg s^-1) compared with the
radio-only MSPs (<P> ~ 4.70 ms and <Edot> ~ 1.0 * 10^34 erg s^-1), while the
spin periods of these two MSP populations are compatible with the log-normal
distributions by the statistical tests. Most rotation-powered MSPs (RMSPs) with
the radio eclipsing (31/34) exhibit the radio+{\gamma} signals, which share the
faster spin (<P> ~ 2.78 ms) and larger spin-down power (<Edot> ~ 4.1 * 10^34
erg s^-1) distributions than the non-eclipsing ones (<P> ~ 4.19 ms, <Edot> ~
2.4 * 10^34 erg s^-1), implying the radio+{\gamma} MSPs to be younger than the
radio-only MSPs. It is noticed that the spin distribution of the
accretion-powered X-ray MSPs shows a clustering phenomenon around ~ 1.6-2.0 ms,
which is not observed in RMSPs, hinting that the RMSPs may experience the
multiple possible origins. Particularly, all the three super-fast spinning
RMSPs with P ~ 1.4-1.6 ms exhibit the non-eclipsing, and we argue that they may
be the distinctive sources formed by the accretion induced collapse (AIC) of
white dwarfs.
