1. Both are in origin the same word. In the 16th century
mettle began to move apart as a separate word used only in figurative meanings, of which the dominant one still current is 'ardent or spirited temperament; spirit, courage', as in the expressions
show one's mettle and
be on one's mettle.
2. The verb
metal has inflected forms
metalled,
metalling in British English, and usually
metaled,
metaling in American English.