Glass 'Armonica' vs. 'Harmonica'
These are different spellings of the same instrument. Franklin originally named his invention the "armonica", after the Italian word "armonia" which means "harmony", in 1761. Franklin's armonica was especially popular in Germany where it was known as the glassharmonika. Right around the time that Franklin's armonica was disappearing from the musical scene, Friedrich Buschmann of Berlin invented the mouth organ "harmonica" in 1821 (he originally called it the Mundäoline), fully 60 years after Franklin invented the armonica. One wonders if he "borrowed" the name of the previously popular but now disappearing instrument for his own invention.
I think it's only right to use the name chosen by its inventor for his invention, especially when the inventor is no less than Benjamin Franklin.
And Franklin's invention doesn't look anything like a "harmonica" anyway!