I'm so used to pressing just S. G. S-S-S-G. R. So I made a shortcut on my keyboard for ALT+S for grease pencil only. From what I read. Grease Pencil scales with Alt+S so it can scale on the normals. Which, not complaining. It just took a few tries before I caved and went and wrote a shortcut so I don't have to remember.
Think of it like this way.... If you've ever used the skin modifier, GP works the same way... selecting two points and using S to scale will "scale them" spacing them further apart. This is exactly the same behavior as scaling any mesh. Alt-S will scale the individual points, giving you a thicker line in the same way it does when you use the skin modifier.