Steampunk definition - http://en.wikipedia.org/wiki/Steampunk
Steampunk is a genre which originated during the 1980s and early 1990s and incorporates elements of science fiction, fantasy, alternate history, horror, and speculative fiction. It involves a setting where steam power is widely used—whether in an alternate history such as Victorian era Britain or "Wild West"-era United States, or in a post-apocalyptic time —that incorporates elements of either science fiction or fantasy. Works of steampunk often feature anachronistic technology, or futuristic innovations as Victorians might have envisioned them, based on a Victorian perspective on fashion, culture, architectural style, and art. This technology includes such fictional machines as those found in the works of H. G. Wells and Jules Verne, or the contemporary authors Philip Pullman, Scott Westerfeld and China Mieville.
Burlesque definition - http://en.wikipedia.org/wiki/American_burlesque
American Burlesque is a genre of variety show. Derived from elements of Victorian burlesque, music hall and minstrel shows, burlesque shows in America became popular in the 1860s and evolved to feature ribald comedy (lewd jokes) and female striptease. By the early 20th century, burlesque in America was presented as a populist blend of satire, performance art, music hall and adult entertainment, featuring striptease and broad comedy acts.
So, if you like the idea of living in the Victorian era, which would you be?
Similarities: Fashion - love of corsets.
Differences: Steampunk focuses more on embracing the technology while Burlesque is more on the artistic side of the era.
Feel free to point out your own differences and similarities.