The terms seem to be used rather interchangeably. Pea prefers the term intelligence, while other seem to like cognition. But there definitely seems to be a difference, both in terms of the process that takes place, and the actors involved. (A quote from Pea)
Intelligence is a thing, a quantity. In this new paradigm it resides outside of the individual, inside artifacts that incorporate the collective experience of a culture. Thus the design of a hammer (a common example) is an expression of distributed intelligence. If we were teaching the principle of hammering in school we might view a rock as an effective tool for accomplishing the task, but that would be counter-productive to the socially distributed intelligence of our culture which has already examined the problem and designed a successful tool in order to accomplish the task. A telephone book contains this sort of distributed intelligence: we don't have to memorize the numbers we want. But a programmable telephone achieves this task even better: if we know how to program numbers into the phone's memory and then retrieve them via a nickname, we no longer have to teach how to use the phone book, and instead can concentrate on how to program the phone.
Cognition is a process. It is the process that leads to a functional outcome of the interaction of individuals and artifacts. But though we are able to view the outcome of this process (the achievement of a task, for instance) we lack tools for measuring it in action.
The actors in these two frameworks are on the whole different as well. In situations of distributed intelligence the interaction is mostly between the individual and the artifact. In situations of distributed cognition the interaction is mostly between individuals, though artifacts may perform the role of mediator.
Though, once again, these terms as seen as relatively interchangeable, they suggest different approaches to studying the use of ODFs: a distributed intelligence approach might choose to investigate how the ODF as an artifact can be used to store retrievable knowledge, whereas a distributed cognition approach might choose to investigate how individuals interact to achieve a common understanding via the use of an ODF.