Technically speaking, there is some leeway - but the distinction comes down to when you go from working with explicit markmaking, to implicit markmaking. You could ostensibly draw all of the knobby bits using explicit markmaking (with greater outlines, as in the demo - which admittedly was done a long time before I developed a more solid idea of how to teach these textural concepts), or you can opt to imply them only with cast shadows.

A good rule of thumb for what is texture, is that it's forms that sit along the surface of a larger structure. What that means, however, is that this is where the grey area begins, where you can choose between explicit or implicit markmaking. Part of the reason you can choose is because this cactus' texture (with the knobby bits) isn't particularly dense, and so to draw each of them with explicit outlines wouldn't result in a lot of density and create unintentional focal points. If however we had a lot more textural forms which were more densely packed, then we'd start to run into problems that would force us into working implicitly.

One thing that may help is that construction focuses primarily on what the viewer needs to know to understand how they might manipulate an object with their hands. Lifting it, turning it, etc. Texture is more about communicating to the viewer what they might feel if they ran their fingers over the object's various surfaces. Both of them do focus on communicating three dimensional information - hence your uncertainty - but separating between things you're going to grab onto vs. things you'll feel with your fingertips can help when choosing which approach to use where.