My understanding of "thinline" as used by Gibson is that it refers to
the shallow bodied models (such as played by Chuck Berry for example) as opposed to the more old-fashioned deeper bodied models so beloved of jazz players but not so well suited for stand-up rock and roll.

The thinline models are 1 3/8" at the edge, the older models would be anything up to 4 3/4".

Why Fender would call any of their products "thinline" is beyond me.

Murray