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Overall all single bonds are sigma bonds and in double or triple bonds. All bonds except the first one are pi bonds. So a double bond has 1 pi bond and a triple bond has 2 pi bonds. Both double and triple bonds have 1 sigma bond.
Sigma bonds are the FIRST bonds to be made between two atoms. They are made from hybridized orbitals. Pi bonds are the SECOND and THIRD bonds to be made. They are made from leftover "p" orbitals