As of now, the FDA has finalized a rule that extends its regulatory authority to all tobacco products, including e-cigarettes, cigars, and hookah and pipe tobacco. So yes, they do (including cigarettes effective August 8, 2016 (fda.gov).

In terms of regulation, I think vape e-cigarettes and regular cigarettes are different because vaping involves using electronic devices so in this case, it’s considered as a combination product while regular cigarettes only contain the bio-compound. (Ex: the delivery/administration part of the electronic cigarette supplied separately from the nicotine-containing product–> medical device).

I think e-cig should be a drug delivery device and require regulations as a medicinal product. Even though the pros outweigh the cons as of now for e-cigs, a lot of people are using it and this number is dramatically increasing, especially in teens: 900% from 2011 to 20115 (cnn.com). Therefore, the potential damage if not taken into consideration carefully can be tremendous.Furthermore, consumers and health professionals also need to be secure in the knowledge that what they are buying contains what it says it contains and meets acceptable standards of safety, quality, and consistency (bmj.com).

References:
http://www.cnn.com/2016/12/08/health/surgeon-general-report-on-e-cigarettes/index.html

E-cigarettes: Good news, bad news

http://www.bmj.com/bmj/section-pdf/187647?path=/bmj/345/7876/Feature.full.pdf
https://www.fda.gov/tobaccoproducts/labeling/rulesregulationsguidance/ucm394909.htm