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