usually it is called a "big band" if it has an extended instrumental section. usually lots of brass instruments. more alto and tenor saxes, trumpets, trombones. a big band sound will usually "blow" you away he he. now add a wind and string section and that is really a bigger band or actually an orchestra.
to me the epitome of a slick big band sound was the GRP All Star Big Band. then again it was just a group of musicians from the GRP stable back in the mid 1990's. for a real big band sound, you gotta go back way into the early 1930's to the 1950's.