Latin, I have a feeling that these two examples are not getting at the difference between the two uses that interest you here. Both of your examples relate more to making an offer; (of course, one must first decide to make such an offer). It seems, however, when using will in the sense of 'a decision made at the moment' (I don't quite know where you found that particular definition), it may be referring to 'willing something to happen'. That is to say, by the force of one's determination, (the power of the will), an action is to be accomplished.