No, triple swing or east coast swing is an essentially in-place dance from the American rhythm family, done to swing music in the 30-40 measures per minute range, and typically using a lot of underarm turns, stop & go passes and perhaps even some separations of the couple.
Quickstep is a travelling dance in the international standard (ie, English ballroom) family done to faster swing music around 50-52 measures per minute, while remaining strictly in hold.
The structure of the music is similar, and there are faster forms of swing (jive, lindy) and slower cousins of quickstep (foxtrot) leading to some overlap in tempo ranges that work for these two general approaches to dancing swing-type music.