My primary question is: what is the importance of Mach number (M) on shock waves? Although I believe confirming and/or answering the below will help clarify my misconceptions.
When a wave moves faster than the local speed of sound ($c_s$) in a fluid, there is a shock wave since the fluid is unable to respond to the moving wave. Even if velocity ($v$) is constant, if pressure ($p$) varies, there can be a shock if the local speed of sound is exceeded (i.e. $ v \geq c_s \rightarrow M \geq 1)$. Therefore, to confirm, isn't there always a shock wave present as long as the wave is supersonic? Does simply the type of shock (e.g. normal, oblique) change as alluded to here?
Also, is there any difference from $M = 1$ shock waves and $M > 1$ shock waves? For example, this article describes a shockless transition from supersonic to subsonic flow, but what does that conceptually mean?