We re-examine the physical relationship between extreme ultraviolet (EUV) waves and type II radio bursts. It has been thought that they are two observational aspects of a single coronal shock wave. However, a lack of their speed correlation hampers the understanding of their respective (or common) natures in a single phenomenon. Knowing the uncertainties in identifying true wave components from observations and measuring their speeds, we re-examine the speeds of EUV waves reported in previous literature and compare these with type II radio bursts and coronal mass ejections (CMEs). This confirms the inconsistency between the speeds of EUV waves and their associated type II radio bursts. Second, CME speeds are found to have a better correlation with type II radio bursts than EUV waves. Finally, type II speeds and their range tend to be much greater than those of EUV waves. We demonstrate that the speed inconsistency is in fact an intrinsic tendency and elucidate the nature of a coronal shock wave consisting of both driven and non-driven parts. This suggests that the speed inconsistency would remain even if all other uncertainties were removed.