i'm sure someone will argue with me, but in america, there is no difference really...
generally speaking "billiards" is used to describe "all" cue sports, while "pool" generally refers specifically to pocket games.
however, there was a time in the u.s. when "billiards" was thought of as respectable "carom" games only - and "pool" was considered to be the shady gambling games played in bars.
in about 1910 or thereabouts, brunswick didnt like the negative implications associated with pool, so they made a declaration to the public that the word "pool" was obsolete and meaningless....
instead they would now use the words "pocket billiards"