My high esteem for halpark's contributions not in question, I believe the explanations regarding "Bohemian" vs. Czech are not the customary wisdom.
Bohemia was the Latin term for what the Germans called (Kingdom of) Böhmen. The Czech (language) term was Czechy. Besides Czechy, there were Morava (Moravia, German term Mähren) plus the remnants of Silesia called Austrian Silesia, which today make up the Czech Republic. Bohemian (in German "böhmisch") as an adjective until quite recently meant the Slavic language we today call Czech. It's really the same thing. Czech Republic means the country comprising the former Austrian crownlands Czechy, Morava and Austrian Silesia.
A similar situation obtains in Austria (although without an issue re the language which is German), as three provinces (Upper Austria and Lower Austria, the latter including the capital Vienna) provided the name Austria to the entire country. Holland was a similar case, i.e., the name of a major province used for the entire country, but there "The Netherlands" seem to have prevailed.
For me, Bohemian means Czech including the Czech language. Germans have a verb called böhmeln to describe a Czech speaking German with a Czech/Slavian accent. The term böhmakeln is also used for the same thing. In the last 50 years or so of the Habsburg Monarchy, scores of Czechs moved to Vienna. Some say that a third of the population was of Czech origin. There was a lot of böhmeln to be heard.