I am an EX smoker, I now vape. I can truthfully say I no longer smoke because I don't inhale combustion products which are commonly called "smoke". I do inhale a substance containing nicotine - same stuff, same safe quality as that used in traditional NRTs. The other ingredients are those used in many foods, and the carrier used for inhalers like nicotine inhalers. All the ingredients bar the flavourings are pharmaceutical grade, and the flavourings are food grade.
My GP was very encouraging when I saw him recently; ideally he wants me to try to slowly cut down the nicotine content but he was very happy that I was vaping instead of smoking, and agrees that e-cigarettes seem to be the best method to date to at least reduce or control an addiction that he understands is one of the hardest to quit (MUCH harder than alcohol in his opinion).
I suppose my vape stick could be described as looking like a cigarette, assuming that cigarettes were about twice the length they actually are, much thicker, weigh about 3-4 times what they actually do, have a purple (or yellow, or green) clear plastic end, and are shiny anodised rainbow in colour. Oh, and don't glow on the end at all. But it IS roughly cylindrical in shape and is held in my hand, so that makes it the same I suppose.
My sister is very strongly opposed to smoking, won't have it near her & the smell makes her ill. But she's happy for me to vape in her house, including the tobacco flavour I sometimes use. She says she can't smell that one, but sometimes she gets a faint whiff of fruit from some of the others.
There hasn't been a cigarette in the house for 3 weeks now but when I walked into my spare bedroom the other day, which I have never smoked in, I could smell the old smoke on the curtains. So I'd assume that the person in the waiting room was someone who still smokes as well as vapes, and the OP was smelling the smoke on her clothing & in her hair.