In Bleach, the term is "reiatsu". In Naruto, it is "chakra". However, all I ever really heard in DBZ is "power level". Is there a more formal descriptive term for the source of their powers or the energy they give off?
The original Japanese term is ki (pronounced the same as "key", written as 気). It can also be spelled chi or qi. The same term is used for a concept in martial arts, though naturally Dragon Ball's version is quite a bit different from this. In the English dubs, this term is never used, and "energy" is used throughout the series.
According to Toriyama, there are 3 components of ki, namely Genki (元気, roughly meaning Energy), Yūki (勇気, Courage), and Shōki (正気, Mind). Ki also can be positive or negative. The various charge up and transformation sequences are all done in order to increase one's ki.
Dragon Ball Wiki has more information on ki in the series.
Power levels measure their strengths alone. Ki measures the energy they have, and to do certain attacks they need to focus their ki, like when Gohan was teaching Videl how to fly, she pushed her ki to the bottom of her feet to fly!
In Naruto, they refer to energy or ki/chi as chakra, but they don't go into detail about the human chakra energy system, but yes, they're basically the same thing. It's all energy, just explained differently.
An interesting relation to DBZ - 7 dragon balls, 7 characters, Goku's grandfather gave him the 4 star dragon ball, or it could be seen as the heart chakra.
Google "chakra" and learn about the human in-built energy system. It ties in body function with human emotion and fundamentally gives us both life and existence.
Shaolin monks use energy in their system of fighting, integrating both body and soul with the focus of their energy through fighting. It's not too dissimilar from DBZ (although DBZ takes to another level, well, because they can :P).
Anyhow that's my 2 cents.