What is the small white card that I was given used for?
First, it is not proof of basic training as required by law. The legislation requires that companies give written authority for people to operate trucks on their premises. Training companies often supply these cards, which people tend to call "permits", to facilitate them doing this. In addition, its easier to carry around than the larger A4 size certificate. If you are on the NORS register you will automatically get one of these.