Recommended (BML&BS) term - Matchbook
The matches packed as a kind of a small book with one or more internal "pages" of "combs" of cardboard or wooden matches. The sticking stripe originally was on the flap that keeps the "pages" of matches together, later, for safety purposes it was applied on the back or face sides of the matchbook and even on the bottom bend.
Such matches are made from the beginning of XX century originally in the USA and Canada.
Before the WW II were also called vest or waistcoat matches because thier slim desing was aimed for carriing them in the waistpocket.
Now in use in many countries, but (except for the North America) mainly as promotional matches, showing sometimes incredible variety of sizes and forms.
Matchbook without matches is called Matchcover or Matchbook cover
"Booklet - alternative but now rarely used term for matchbook. Probably still in use because of its inclusion in the name of the British Matchbox Label and Booklet Society whose original members agreed to this title in 1945.
Matchbook - a folded card enclosing a comb of bookmatches fixed to it." (definitions from the BML&BS site)
Equvivalent Russian term Ασκλες
 Matchbook from "The World Wonders" set (Tailand) From collection of Victor Raldugin |
 Australian promotional matchbook From collection of Stanislav Dmitriev |
 Matchbook from "280 years to Eketherinburg" souvenir set From collection of A. & A. Chekushins |
 Promotional matchbook of insurance company From collection of A. & A. Chekushins |