Answer:
Democritus came up with the idea that there was an ultimately small bit of matter that could not be divided any further. He called this "atomos" for "indivisible".
Much later, what we call the atom was discovered. As researchers at the time thought that it was the smallest bit of matter, they called it the "atom", after the Greek "atomos".
Ever after, poor Democritus has been called wrong, as teachers gleefully point out that the atom can be divided! Yet Democritus never said that what we call the atom was the smallest bit of matter. He simply hypothesized that there would be such a thing as an indivisble bit of mattter, and it was that and that alone he called "atomos".
So the Greeks did not believe any one thing was the tiniest bit of matter. They simply believed that there was such a thing, regardless as to what exactly it would turn out to be.