That's pretty much right. A few notes:
"Phantom power" (at least as I've heard the term used) refers specifically to the particular method of providing power by providing an equal +48 volts (across 6.8 kohms) on the two legs of a balanced line. That is, the term really refers to the particular method of supplying the power, rather than what the power is being used for.
As noted, "true" (non-electret) condensors need power to charge their capsules. They commonly get it from phantom power.
Condensor mics (both electret and "true") typically also require power for the preamplifier that's in the mic. The signal from the capsule is very small (and the wrong impedance), and needs to be amplified before it's sent down the mic cord. They often get this from phantom power, but not always. Many electret mics use batteries for this power. Tube mics (the preamplifier in the mic uses a tube) typically require their own special power supply, in place of phantom power.
There's also at least one ribbon mic (I think one of the newer Royer models, if I remember correctly) which has a preamplifier in the mic body, and uses phantom power for it.
There are some devices other than mics which use phantom power, too. For example, some active direct boxes are capable of being powerd with phantom power. I believe the Sansamp Bass Driver (which, so far as I understand it, is an active direct box with some signal-modifying / distortion circuitry in it) can use phantom power or a wall wart.