Smooth/Hidden Lines in SketchUp
Understanding the difference between smoothing out and hiding lines in your SketchUp model.
Step 1: Default
Depending on your style settings, edges and profiles should be on. As you can see, the edges in the model are clearly visible. selecting a face will only select that part of the geometry. The same goes for selecting the edge itself.
Step 2: Eraser Plus
Either select the Eraser icon from the toolbar or simply press E on your keyboard. The Ctrl, Alt, and Shift keys act as toggles for Soften/Smooth, Unsmooth/Unhide, and Hide, respectively. The eraser icon will change based on your selection.
Step 3: Hidden
When you hide lines, the geometry still behaves as it did before. You'll notice profiles are missing and you can still select the individual faces. You will not be able to select edges. This is important because the push/pull tool will still work, but whatever you extrude will now have visible edges.
Step 4: Smooth
When you smooth out lines, the edges that are left are notably softer, almost rounded off. Profiles remain and when you select a face, it selects some of the adjacent geometry as well. This is important because the push/pull tool will not work on curved surfaces, which is essentially what you've created by smoothing out these lines.
Step 5: Side by Side
Here are all 3 side-by-side.