Mishnah 3 in Maseches Peah deals with where in the field the peah must be left. Peah is usually thought of as something given at the end of the field, at its edge or in its corner, since the wording of the Torah, "lo sechaleh pe'as sadcha" - "you shall not finish off the corner of your field" - seems to point to the end of the field. The Mishnah teaches a novel ruling: peah may be given from the very beginning of the field, from the moment the harvesting starts, and even from its middle.
The view of Rabbi Shimon:
Rabbi Shimon adds a condition: this works only if at the end of the field he leaves the proper measure, one sixtieth. There are two ways of understanding his words:
One sixtieth of the entire field.
One sixtieth including the peah already given at the beginning or in the middle of the field.
What, then, is gained by giving peah at the beginning or in the middle?
According to the view that combines the two gifts, the benefit is clear. But according to the first view, that he must leave at the end one sixtieth of the entire field, it would seem that the earlier gift accomplished nothing at all - for if he left the full measure at the end, why should the other portion also count as peah?
The difference concerns the obligation of Terumah and maasros: something that has the status of peah is exempt from maaser, and no Terumah or maasros need be separated from it, whereas something that is not considered peah is obligated in them. Therefore Rabbi Shimon says: if he left the proper measure at the end of the field, then what he gave earlier as peah retains its halachic status as peah as well, and carries no obligation of Terumah and maasros.
The view of Rabbi Yehudah:
Rabbi Yehudah offers a different perspective: if he left at the end of the field at least one stalk, he can rely on it, and give the rest of the peah at the beginning or in the middle of the field. In this way the principle that peah is given at the end is upheld, and nevertheless he is not required to give the full measure there, but may give it at the beginning or in the middle, provided that it is still attached to the ground, and that at least one stalk remains at the end of the field.
"V'im lav, eino nosen ela mishum hefker" - and if not, what he gives counts only as hefker (ownerless property):
If not even a single stalk remains at the end of the field, what he gives is not considered peah. One who wishes to be exempt from maaser can do so only by giving the produce to the poor as hefker: he declares that it has no owner, and anything that is hefker is not obligated in Terumah and maasros. In this way he gives to the poor under the definition of hefker.
What, then, is the difference between hefker and peah?
What they share: both are exempt from maaser, and both may be given to the poor.
The difference: plain hefker is permitted even to one who is not poor - to a wealthy person, who may not take peah but may take hefker; whereas something that has the status of peah is permitted to the poor alone.