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I know I found an explanation of the difference once before, but I can't seem to locate it. IIRC, addcore_national has no nationalism risk while addcore_casus does, but I don't recall what addcore_claim does differently.
National is regular core.
Casusbelli is only giving you permament CB on the owner of the province.
Claim starts only with giving you CB but after nationalism expires it turns into actual core. It's 30 years in vanilla. Can be changed in defines.txt by editing this bit: