What's the difference between 'constructivism' à la Latour, Stengers, Whitehead and 'realism' à la Bryant, DeLanda, Morton, etc.? Specifically, what's the difference with respect to their uses of scientific knowledge?
The 'realists' take science to be a content provider – that is, science provides and certifies a more or less stable list of entities with which the philosopher can justifiably populate the world as they see fit.
The 'constructivists' also want to populate the world with a wide range of entities and to grant these beings their autonomy, their powers, their dignity. However, they (a) are not prepared to grant science the right of unilateral list-writing, (b) they emphasise the instability of the list (as a necessary precondition of science itself as much as anything else) and (c) they insist, above all, on making science a constituent producer – that is, the fact of scientific production as an ongoing process must be factored in to any substantial discussion of scientific facts, including their mobilisation in world-population exercises.
It is not that scientific facts are reducible to their construction or instauration (that is, this is not relativism in the vulgar sense) but rather that discussing scientific facts severed from their subtending networks results in a dogmatism that precludes politics and a simplicity that does no justice to science. In other words, populating the cosmos is a shared interest but opinions differ on how it is to be done.
There's far more to this dispute than this one, only partially explicated difference, of course, but this is a key part of it, I think. For one side 'realism' means that any discussion of scientific facts implies an understanding of scientific processes and that this implication must be made explicit in the discussion; for the other side 'realism' means that one can and should ignore this implication and sever, at least in rhetoric, the facts from their networks. It's the difference between a realism that thinks it misleading or even meaningless to discuss scientific objects in abstraction from the processes that stabilise them as knowable and hence articulable entities and a realism that thinks it the quintessence of realism to do just this.