This is actually a great question and one that I'm often asked. There is an easy way to actually visually see the difference between vaping and cigarettes.
Grab a smoker and some tissue. Fold the tissue in half, then ask the smoker to blow through the tissue. Ask them to do this three more times. You'll be absolutely shocked at the yellowing left behind on the tissue paper. Now, repeat the process with your e cigarette, do it 5 or even 10 times. You should notice, no stain And if for some reason there was a stain, switch liquids because I've done this test more times than I can count for people and I've never stained tissue with an e-cigarette.
On a side note, as british born guy, I'm pretty self conscious about my teeth. (Cavity free my whole life!). When I was a smoker, no matter how hard I tried, I generally suffered from yellowing. These days I'm pretty happy with how white my teeth are. It's been 8 years now and my teeth look great. (And any yellowing that I do have is likely from coffee).