As for an example of why visiting new place might be confusing, refer to Greg's explanation (and a very nice one, by the way) of how to name techniques. In one style I studied, those names would still be 'missing' what I came to think of as the 'middle name' of the technique. For example, in his system a technique might be Katate tori kokyu nage (with perhaps an omote or tenkan) ki no nigare. In the one I studied, the same teachnique could be:
Katate-tori kokyu nage
a. tenchi nage irimi
b. tenchi nage tenkan
c. tekubi tori irimi
d. tekubi kosatori irimi, jodan style
e. tekubi kiri irimi, gedan style
f. tekubi kiri, chudan style
g. tekubi tori tenkan
h. ude oroshi irimi
i. ude oroshi tenkan
Imagine trying to square those conflicting names away while still working on getting a square knot to stay tied thorugh an entire class...
visiting new places is great, I think, just be sure you go with a very open mind and the knowledge that there is no one absolute way to do anything, from tie your hakama to get a partner to name a technique to do the technique.