We have studied the aperiodic X-ray timing and color behavior of the accreting millisecond pulsars SAX J1808.4À3658, XTE J1751À305, XTE J0929À314, and XTE J1814À338 using large data sets obtained with the Rossi X-Ray Timing Explorer. We find that the accreting millisecond pulsars have timing properties very similar to atoll sources and low-luminosity bursters. On the basis of the correlation of timing and color behavior, SAX J1808.4À3658 can be classified as an atoll source, and XTE J0929À314 and XTE J1814À338 are consistent with atoll sources, but the color behavior of XTE J1751À305 is different. Unlike the color in other atoll sources, the hard color in the extreme island state of XTE J1751À305 is strongly correlated with soft color and intensity and is not anticorrelated with any of the characteristic frequencies. We found previously that the frequencies of the variability components of atoll sources follow a universal scheme of correlations. The frequency correlations of the accreting millisecond pulsars are similar, but in the cases of SAX J1808.4À3658 and XTE J0929À314 they are shifted compared with those of the other atoll sources in a way that is most easily described as a shift in upper and lower kilohertz quasi-periodic oscillation (QPO) frequency by a factor close to 1.5. However, we note that the shift in the lower kilohertz QPO frequency is based on only one observation for SAX J1808.4À3658. XTE J1751À305 and XTE J1814À338, as well as the low-luminosity bursters, show no or possibly only small shifts.