Greek word elements are parts of words that have their origin in ancient Greek. A good example is meta, ancient Greek for about. Metaphysics has acquired a well-established meaning, but people freely apply meta to other things: for instance, meta-data for data about data. Another example is the pair homo and hetero, same and different, which you will find as prefixes in many English words, for example homosexual and heterosexual.
A Latin root is the Latin word from which an English word is derived. For example, pedestrian has the Latin root pedum, foot.
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