There is no such thing as QSP Magazine. QSP is a fund raising organization that helps groups such as the Girl Scouts of America or local schools raise funds by selling a number of items, including subscriptions to unaffiliated magazines such as People, Time and Sports Illustrated.
QSP was acquired by Great American in 2012, and the latter company handles all of QSP's operations as of August 2015. The company offers a number of "packages" of magazines to sell, each geared toward a specific market. Magazine renewals can also be purchased through the fund raiser, with the new subscription kicking in whenever the old one expires. Other items sold by QSP/Great American include cookie dough, nuts, candy and gift wrap.