Large-scale, wave-like disturbances in extreme-ultraviolet (EUV) and type II radio bursts are often associated with coronal mass ejections (CMEs). Both phenomena may signify shock waves driven by CMEs. Taking EUV full-disk images at an unprecedented cadence, the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory has observed the so-called EIT waves or large-scale coronal propagating fronts (LCPFs) from their early evolution, which coincides with the period when most metric type II bursts occur. This article discusses the relation of LCPFs as captured by AIA with metric type II bursts. We show examples of type II bursts without a clear LCPF and fast LCPFs without a type II burst. Part of the disconnect between the two phenomena may be due to the difficulty in identifying them objectively. Furthermore, it is possible that the individual LCPFs and type II bursts may reflect different physical processes and external factors. In particular, the type II bursts that start at low frequencies and high altitudes tend to accompany an extended arcshaped feature, which probably represents the 3D structure of the CME and the shock wave around it, rather than its near-surface track, which has usually been identified with EIT waves. This feature expands and propagates toward and beyond the limb. These events may be characterized by stretching of field lines in the radial direction, and be distinct from other LCPFs, which may be explained in terms of sudden lateral expansion of the coronal volume. Neither LCPFs nor type II bursts by themselves serve as necessary conditions for coronal shock waves, but these phenomena may provide useful information on the early evolution of the shock waves in 3D when both are clearly identified in eruptive events.