Stage cigarettes have been around for over a century and exist solely to give the impression that someone is smoking. (i.e. they don't contain nicotine).
e-cigarettes have only been around since 2003 (although an earlier version was patented 40 years previously) and the whole point of them is to give users a nicotine fix.
So, clearly, they're NOT the same.
However it is actually possible to obtain non-nicotine cartridges for e-cigarettes, so a model that looks like 'the real thing' could be used as a stage prop if required.
More options here:
https://www.mallatts.com/blog/guide-fake-stage-cigarettes-for-nonsmoking-actors