Illustrated Glossary of Organic Chemistry

Alkene: A functional group characterized by a carbon-carbon double bond. When the carbon-carbon double bond is fully contained within another functional group such as a benzene ring, we do not say the more complex functional group is an alkene.

General alkene structure.   
Ethylene, the simplest alkene.   
Z-3-iodo-2-octene, a disubstituted internal alkene.