The story (and Max Miller's claim, at least in his act) was that the blue book contained "adult" jokes and the white one contained those that were suitable for family audiences. Assuming that he was performing for an adult audience, he would ask if they wanted the blue book or the white book. Naturally, they nearly always went for the blue one.
I've even heard it said that this is the origin of the use of the word "blue" to describe adult humour, films, etc. But I've never been entirely convinced that Max Miller's two books actually contained jokes (as Bob Monkhouse's equally famously did) or whether they were just props.
© Haydn Thompson 2022