By 3rd level, a Paladin gains the following ability (PHB, pg. 85):
Divine Health: The divine magic flowing through you makes you immune to disease.
Does this protect against both common AND magical disease?
There is no differentiation between the two. Disease is simply disease in the relevant entries (which I can't find anymore). A few spells afflict you with disease; sickly common folk may be diseased, and certain magical aura's on enemies may inflict a diseased state. Since these all count under the 'Disease' umbrella, and the Paladin trait simply says a magical energy is making you immune to disease... I assume this is read as "Immune to [all] disease."