I have deeply checked but couldn't find the difference between Q1 and S1 visa.

Braian, the Q1 type is issued to those who are family members of Chinese citizens or of foreigners with Chinese permanent residence and intend to go to PRC for family reunion, or to those who intend to go to PRC for the purpose of foster care.
S1 is issued to those who intend to go to PRC to visit the foreigners working or studying there to whom they are spouses, parents, sons or daughters under the age of 18 or parents-in-law, or to those who intend to go to PRC for other private affairs.