As I understand Brinks actually wraps coins, String & Sons makes the machines and supplies the paper they use. They don't wrap themselves. Whether you get plastic or the String & Sons paper depends on what machines the firm doing the wrapping happens to be using.
Maybe his is why the actual Brinks armored truck might deliver pennies that are Brinks rolls one week and then the next week the rolls and boxes are labeled String and Son?
Either they are using multiple rolling machine or contracting out having some coins rolled by another company.
Does some else have some insight other than this?