If someone doesn't take off terumah and ma'aser, their produce is TEVEL. This means it is absolutely not allowed for a Jewish person to eat it (unless he gives the terumah and ma'aser).
There were some people who were good Jews, who wanted to keep the Torah but did not always know how. Someone like this was called AM HA'ARETZ. Since the rabbis didn't know if they knew enough to do teruma and ma'aser correctly, they said their produce was DEMAI. Since we weren't sure, someone buying from an Am Ha'Aretz would also have to take of teruma and ma'aser.
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