There are some differences, a US friend of mine did law in the UK which meant she could work anywhere from Finland to Greece. But when she passed the New York bar she couldn't work in New Jersey.
In contrast, one doesn't even need a law school degree to be able to take the bar exam in any US state. (admittedly it's almost impossible to pass without one).
Not quite: In a number of US states, a prerequisite to taking the bar exam is either graduation from an ABA-accredited law school, or a foreign law degree with additional training in a U.S. school. See Chart III at http://www.ncbex.org/fileadmin/mediafiles/downloads/Comp_Gui... and the supplemental remarks afterwards, also Chart X.