I always took it to mean the same category of distinction made in biological categories. That is, 'people' means a simple plural person, where "persons" means a plural of person categories.
Like 'fish' means multiple fish, but 'fishes' means multiple species of fish.
Then saying 'these persons' would essentially mean 'these groups of different kinds of people.' (But that could also just be implicit regardless of your word choice.)
But... you can also use 'person' to mean the body of a person, so that 'persons' could mean multiple bodies. "They carried the weapons on their persons," for instance. Akin to how 'mice' is the plural of the animal, but 'mouses' is the plural of the computer peripheral.
Like 'fish' means multiple fish, but 'fishes' means multiple species of fish.
Then saying 'these persons' would essentially mean 'these groups of different kinds of people.' (But that could also just be implicit regardless of your word choice.)
But... you can also use 'person' to mean the body of a person, so that 'persons' could mean multiple bodies. "They carried the weapons on their persons," for instance. Akin to how 'mice' is the plural of the animal, but 'mouses' is the plural of the computer peripheral.