Brand positioning describes how a brand is different from its competitors and where, or how, it sits in a particular market. These differences might be real ones, but not have any motivating qualities about them. They would still, however, give a brand a 'positioning' in a market. For example, a beer might have the positioning of being an 'Alaskan beer', but this might not be very motivating to the consumer.
If the positioning of being an 'Alaskan beer' is motivating to consumers then this value begins to accrue propositional values as well as positional ones. It begins to literally 'proposition' the consumer. Much of marketing research is in fact involved in the task of evaluating whether the positional characteristics of a brand (or a product) can be transformed into propositional ones. This is, in many ways, what marketing is.
The two terms - positionings and propositions - are often confused together because, of course, many values and terms have BOTH some positioning and some propositional aspects. The terms 'economy' and 'premium' are good examples of this. They can be used to describe a brand's positioning in a market, but they also deliver meaning and motivational qualities to consumers as well. Despite these degrees of overlap, the concepts of positioning and proposition are, however, still working along quite distinct dimensions. A positioning describes how a brand is different in a market. A proposition encapsulates what it might mean to a consumer.