https://dd214direct.com/veteran-need-guncc-permit/ has some additional details, but largely agrees with you; some states also lower the age requirement for veterans.

Louisiana recently passed a law allowing vets to concealed carry without a license https://www.audacy.com/wwl/news/local/concealed-carry-law-could-be-model-for-other-states , but this definitely seems like the exception and not the rule