Hi Nils,
Apology for not writing your name right the first time.
As the hint on directNormalRadiation says, it is the radiation received on a surface perpendicular to the sun ray coming from the skydome. Therefore, only direct normal radiation should match, as you pointed out.
globalHorizontalRadiation and diffuseHorizontalRadiation are radiation on a horizontal surface, so they will differ. Attached image should give you a clue. You can test this using Ladybug.
Take the total of globalHorizontalRadiation. From that deduct the total of diffuseHorizontalRadiation. That number will be less than the total of directNormalRadiation.
-Devang
