The Mishnah opens: "HaMachnis ma'os ve'omer: Harei eilu lishkali" - a person who collects coins one perutah at a time, in order to accumulate enough for his half shekel, and says: this money shall be for my half shekel. The question is: what is the status of the money if in the end he accumulated more than he needed, more than a half shekel?
The dispute between Beis Shammai and Beis Hillel:
First, what is a 'nedavah'? In the Beis HaMikdash there were shofaros - charity boxes into which people placed coins for various purposes, and this money was used for olah offerings. Whenever nothing was being offered on the altar and no offerings had been brought, they would bring these nedavah olos, which came from the surpluses of various offerings.
"Beis Shammai omrim: mosaro linedavah" - the surplus money beyond the half shekel goes to nedavah. This is because Beis Shammai hold 'hekdesh be'ta'us hekdesh': if a person consecrated something by mistake, it is nevertheless consecrated and has the status of hekdesh. That is exactly what happened here - with every single perutah he set aside, he thought it was going to hekdesh, to his half shekel. In the end it turned out that this was not needed, and even though it was a mistake, everything beyond the half shekel belongs to hekdesh, and it is therefore used to bring a nedavah offering, an olah.
"U'Beis Hillel omrim: mosaro chulin" - the surplus is chulin, because Beis Hillel hold 'hekdesh be'ta'us eino hekdesh': whatever was consecrated by mistake has no sanctity. Therefore all the surplus money is chulin and is not considered hekdesh.
"She'avi mehen lishkali":
What is the ruling if he used a different wording: "she'avi mehen lishkali" - not that this money itself is for the half shekel, but that from this money he will bring his half shekel? Here "shavin shemosaram chulin" - Beis Shammai and Beis Hillel agree that the surplus is chulin, since he stated clearly that he would bring a half shekel out of this money, and consequently the rest of the money beyond that is certainly chulin.
Regarding a chatas offering:
"Eilu lechatas" - one who says about the coins he is collecting that they shall be for a chatas offering that he is obligated to bring, "shavin shemosaran nedavah": Beis Shammai and Beis Hillel agree here that the surplus is considered nedavah and is not chulin.
"She'avi mehen lechatas" - one who says that from this money he will bring the chatas, "shavin shemosaran chulin": here all agree, just as we said regarding the shekel, that the surplus is chulin. For he designated for the chatas only the amount required for it, and regarding anything beyond that he made clear that it would not be hekdesh, and therefore it is chulin.
In summary: when he says "harei eilu lishkali," Beis Shammai and Beis Hillel disagree about the status of the surplus - nedavah or chulin - and the root of the dispute is whether hekdesh by mistake is hekdesh; when he says "she'avi mehen lishkali," all agree that the surplus is chulin; and regarding a chatas, with "eilu lechatas" the surplus is nedavah according to all opinions, and with "she'avi mehen lechatas" the surplus is chulin according to all opinions.
One question remains: why, when he says "eilu lechatas," does Beis Hillel agree that the surplus is nedavah, while regarding the shekel they said that the surplus is chulin? We will see this in the next Mishnah.