Xenharmonic music is a type of microtonal music that uses strange or foreign harmony. It generally does not refer to microtonal music that is similar to twelve tone equal temperament.
Linguistically, this is kind of a mess. Xenharmonic music is a useful term, but not very precise. Whether a certain tuning is xenharmonic can depend on how it's used or how it's perceived by the listener.
The term xenharmonic music may be vague, but the attitude of a composer who identifies his music as xenharmonic may be more clearly defined. Frequently, such a person will explore types of musical expression that is new and experimental.
Many traditional microtonalists look to the past for inspiration and take a very conservative approach to their selection of scales or musical styles. They may view modern twelve tone equal temperament as a deviation from pure and natural principles and long to experience the musical joys of simpler times. This is usually not xenharmonic music.
A xenharmonicist tends to go in the opposite direction, perhaps exploring nontraditional, justly tuned intervals or using scales with unusual dissonances. A truly enthusiastic xenharmonic composer will take nothing for granted. He may try music that weakens or eliminates the concept of the octave. He may use scales that feature severely detuned fifths or that use the tritone in unexpected ways.
These terms can give the false impression that these two different types of microtonal music are mutually exclusive. I prefer to view microtonal music as more of a spectrum, where some is more xenharmonic and some is more traditional. It's somewhat rare and, probably, unwise for an individual to devote all their attention to one extreme end of this spectrum.
Microtonalists are an extremely varied group of people that are lumped together in one inconveniently vague term. Many people, including myself, have spent time trying to think of better, more precise terms to describe our craft, without much success.
Maybe this is OK. We are all in the same boat, regardless of our differences. Many people are unaware that we even exist. Inconveniently vague and simplified terms may be all that the public can handle at the moment. Give them a little time time to discover us, and then precise distinctions may become more important.
I for one, am not too concerned about these differences. I have great respect for anyone who is willing to challenge the supremacy of twelve tone equal temperament. Some of our ideas may be flawed. We may make some mistakes, but in music, these mistakes can teach us as much as our successes. If we are humble we can all learn from each other.