Since Pesach involved only a partial redemption of the Jews and the destruction of Egypt, and as the same sacrifice was offered in the Temple on every day of the holiday (as opposed to Sukkot), only "Half" (or Partial) Hallel is recited on all of the last six days of Pesach.

Do you say Hallel on Chol Hamoed Pesach?

Hallel and Mussaf prayers are said on these days, as on Yom Tov, although on Chol Hamoed of Passover, an abridged form of Hallel is recited. ... The tachanun prayer is omitted.

Why is Song of Solomon read at Passover?

In modern Judaism the Song is read on the Sabbath during the Passover, which marks the beginning of the grain-harvest as well as commemorating the Exodus from Egypt. Jewish tradition reads it as an allegory of the relationship between God and Israel; Christianity, as an allegory of Christ and his bride, the Church.