Variability is one of the classic features of active galactic nuclei (AGNs). The normalized structure function was applied to distinguish variability samples from the Owens Valley Radio Observatory, the All-sky Automated Survey for SuperNovae and Fermi. A power-law function model was selected to fit the structure functions of samples of three bands. We present the available samples of three bands, and by integrating two parameters, we obtain ideal discrimination results for three bands. Meanwhile, the differences between BL Lacertae objects (BL Lacs) and flat spectrum radio quasars (FSRQs) of Fermi and non-Fermi samples are well verified. The results show that the improved structure function can effectively distinguish samples of radio, optical, and gamma-ray. Additionally, BL Lacs and FSRQs in both Fermi and non-Fermi samples can be distinguished. The conclusion obtained through the distinction of structural functions in different bands supports that the variabilities in the three bands are caused by different physical mechanisms respectively: the samples in the optical band are radio quiet AGNs, and their variability is mainly caused by the fluctuations of the accretion disk, and the samples of the radio band and gamma-ray band are radio loud AGNs whose variability is mainly caused by relativistic jet radiation. This conclusion conforms to the unified standard interpretation of variability about AGNs. Using these two parameters, we verify that there is no fundamental difference between Fermi and non-Fermi BL Lacs, while significant differences exist between FSRQs. However, the power exponent of the two can well distinguish BL Lacs.