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