Is TheoCaching a part of Geocaching? If so, how?

Yes. The Geocaching community is very open to new variations. In facts, Geocaching strongly encourages it (see www.geocaching.org). TheoCaching uses elements of Geocaching, but with a spiritual twist of sorts, in which the "cache" or "treasure" is the shared journey. Of course, other versions of TheoCaching may include a more traditional geocaching-type container at the mid-way point of the journey through which tokens of the journey may be exchanged.