I believe tape is one of those words that used to have a more broad application, and then narrowed in on a new product.

I sew a bit, and "bias tape" is non-adhesive, thin strips of cloth used for hems and other edge applications. Measuring tapes likewise aren't adhesive and have probably been around for about as long as measuring has - my old art history class is ticking my brain, reminding me of measuring rods and ropes being the symbols of power and rulership in extremely ancient Mesopotamian, Egyptian, etc art.

According to this link, it is indeed an old word that meant "thin strip of cloth used for tying, measuring, etc". So it sounds like we're just doing tape dirty by forgetting it's one of the OGs of civilization.