[Typo3] Template problem again

[Martin S]

How does one use one template to several sites?
(Sounds like a stupid question)

I use template A for site 1 and modify aspects (like background image).
Then I make another template directory with name B with the same basic files 
as in A, but modify these to suit site 2.

Going to site 2 brings me the modifications for site 1....

Tree:

fileadmin
templates
A 
files modified for site 1
B
files modified for site 2 - same base as for A

Obviously I'm doing something wrong...


Regards,

Martin S