We explore UV and optical variability signatures for several hundred members of NGC 2264 (3 Myr). We performed simultaneous u- and r-band monitoring over two full weeks with CFHT/MegaCam. About 750 young stars are probed; 40% of them are accreting. Statistically distinct variability properties are observed for accreting and non-accreting cluster members. The accretors exhibit a significantly higher level of variability than the non-accretors, especially in the UV. The amount of u-band variability correlates statistically with UV excess in disk-bearing objects, which suggests that accretion and star-disk interaction are the main sources of variability. Cool magnetic spots, several hundred degrees colder than the photosphere and covering from 5 to 30% of the stellar surface, appear to be the leading factor of variability for the non-accreting stars. In contrast, accretion spots, a few thousand degrees hotter than the photosphere and covering a few percent of the stellar surface, best reproduce the variability of accreting objects. The color behavior is also found to be different between accreting and non-accreting stars. Typical variability amplitudes for accreting members rapidly increase from r to u, which indicates a much stronger contrast at short wavelengths; a lower color dependence in the amplitudes is instead measured for diskless stars. We find that u-band variability on hour timescales is typically about 10% of the peak-to-peak variability on day timescales, while longer term (years) variability is consistent with amplitudes measured over weeks. We conclude that for both accreting and non-accreting stars, the mid-term rotational modulation by spots is the leading timescale for a variability of up to several years. In turn, this suggests that the accretion process is essentially stable over years, although it exhibits low-level shorter term variations in single accretion events.