There are several different viewing options which involve wireframe displays.
- Clicking on the Viewport Shading buttons in the top-right corner of the 3D view. Of the four, the one on the far left, the first of the four, is Wireframe. This shows wireframe displays while turning off all solid shading, making all solid faces invisible.
- As an alternative approach to achieving the above, pressing z in the 3D View to bring up the Viewport Shading pie menu, and choosing Wireframe.
- Simply going into Edit Mode for any selected, solid-shaded object will automatically show a wireframe display. The above-mentioned Viewport Shading options work in Edit Mode as well as Object Mode.
- If you go to the Overlays dropdown at the top-right of the 3D View (immediately to the left of the Viewport Shading buttons), you can turn on a Wireframe display for all objects in your 3D View. This has no effect on how anything else appears. It only adds a wireframe outline on top of otherwise solid-shaded forms. This function is technically accessible in both Object and Edit Mode, however it seems to have no visual effect in Edit Mode. Furthermore, the checkbox only exists in Edit Mode if you are also in Solid shading mode. If you are in Wireframe shading mode while in Edit Mode, and go to the Overlays dropdown, the Wireframe checkbox does not even exist! This could certainly lead to confusion. It might have been clearer to new users if this checkbox were merely grayed out in this case, instead of completely missing.
- Wireframe displays can be invoked on an object-by-object basis by going to the Object tab in the Properties Panel (not the Object Data tab), for any selected object, expanding the Viewport Display section, and changing the Display As dropdown to Wire. This can be helpful when you don't want everything to be displayed the same way at the same time.
In addition to the above, you can create an x-ray view of a selected object with Alt + z to make the object display as translucent even without it having a wireframe overlay currently. Wireframe overlays can be used in addition to this x-ray feature. The x-ray feature works both in Object and Edit Mode. I mention this feature because, your first picture above has some graininess to it that I don't visually understand, but I wonder if the x-ray feature may be involved. Your picture below, which I gather is your version, doesn't have this graininess, so I wonder if when you activate the x-ray feature, you may have a display that matches the coach's version.
Hope this helps.