Timber and timbre have distinctive definitions. They are not simply the result of Americanization (or Americanisation, if you like) of the same word.
Gray vs. grey
Alumna, alumnae, alumni, alumnus
Learned vs. learnt
Fish vs. fishes
Its vs. it’s
Center vs. centre
Practice vs. practise
Affect vs. effect
Canceled vs. cancelled
Realise vs. realize
Than vs. then
Favorite vs. favourite
Adviser vs. advisor
Timber and timbre have distinctive definitions. They are not simply the result of Americanization (or Americanisation, if you like) of the same word.