Hi SisterLuna, you have it right. *Onde* is used in a "scientific" sense, but I'd also refine this further and say that it's used in a mathematic or calculational sense/application. *Vague* is used for day to day "representations" of a wave-like behavior, i.e. things that have a notional (inexact), cyclical or periodic rhythm (ocean waves, waves of crowds exiting a station with the arrival of trains, etc.).
It may help you to think of *onde* as used for discrete wave forms/phenomena that can be represented by a mathematical equation (like sine wave=l'onde sinusoïdale or wavelength=longueur d'ondes) instead of "figurative" waves.
A heat wave is an ecologic/climatic phenomenon, but it is not a mathematic one. [i.e. the phenomenon can't be represented as a graphical equation where you can determine a certain value (say, temperature) based on its position on the curve].