It seems that in the US in the early to mid 20th century Burlesque and Vaudeville went together. Milton Berle, Phil Silvers, Red Skeleton, the Marx Brothers to name a few did vaudevillian acts that also included burlesque performances. Basically live variety entertainment.
I don't think I'd agree with Sir Richard that "early to mid 20th century Burlesque and Vaudeville went together." From my reading on the subject, Vaudevillians looked down on their Burlesque compatriots and the performers operated in different theatrical circuits/wheels targeted to different audiences.
Vaudeville was promoted as "family" entertainment to build up the audience with "respectable" women and children - acts would get in trouble if they got too racy. Burlesque was geared to a more adult male audience and local ordnances would often affect the level of bawdiness that could appear on stage (Boston shows being much tamer than other cities and the Western wheel being noted as more racy than the Eastern).
While it was not unknown for Vaudevillians down on their luck to appear under assumed names in Burlesque shows and for a number of male burlesque comics to "move up" to Vaudeville, there was a general "class" distinction between the two artforms at that time.
historic male Burlesque
Linear Mode
