Contemplation versus meditation
One way I've seen this difference defined was in a text about Dzogchen "meditation of non-meditation". They said that traditional meditation involves conditioning or shaping the mind, while contemplation involves watching without trying to manipulate. Dzogchen non-meditation was characterized as a type of contemplation, rather than regular meditation. Incidentally, the Zen meditation I was taught (a Korean type of Shikantaza) had also emphasized this non-manipulative aspect.

I don't think this is what "contemplation" means in your text though. It seems like when they refer to "contemplation" they mean "mulling over" as opposed to "seeing" directly. So it seems your book is making the same point as my sources ("just watch what's here") while confusingly using the opposite words to convey it.