This is only partially true. The chords in A natural minor will be the same but it's much more common to hear a dominant fifth using the harmonic minor so you would change the Em to E especially in classical and jazz music.
nit: jazz is the melodic minor (raised 6th as well). Such a beautiful sound; and the modes allow you to get the altered scale (7th mode of melodic minor) which sounds good(?) over the dominant
