[frontierrots]

Personally (and this is just MY opinion) the pup you describe as "willing" ie willing to to as bid for no reason other than asked (I'm talking pre training here not a trained dog) "I" would call extremely biddable and a tad soft.

The pup you describe as having "low willingness" I see as a pup that uses it's brain and rationalizes that payment is required in the learning process (ie treat) in order to justify getting shut in a crate as a good thing. An independent thinker, a problem solver, a pup that does not need me to tell it what to do every second

While the first pup (your high willingness) would be an easy pup for a novice to train, it's not the pup "I" would want