Yes, ewie, a mishmash, but I do see something they have in common — as long as we assume that "plaster" is the 'BrE thing' (what my gran called "sticking plaster") — they can all be very hard to remove from skin.
Ink-stained fingers were very common in the days when fountain-pens were the norm. The adhesive from old-fashioned plasters clung to the skin like glue and needed a scrubbing brush and solvent to get it off. And presumably self-tanning lotion stains skin, 'cos it's designed to!
Whereas the kind of plaster you slap on walls comes off skin easily with soap and water, and wouldn't need a special product.
If I'm right, the ad does seem rather outdated (yes Kate, weird even). The ballpoint pen put an end to schoolboys' ink-stained hands, and modern plasters don't leave adhesive gunk on your skin (even if they do still rip a few hairs off!). As for self-tanning lotion, ummm, I don't know — I've never used it.
Ws👁 Smile :)