The denial of actualism is possibilism, the thesis that there are some entities that are merely possible: these entities exist (in the same way that ordinary objects around us do) but are not to be found in the actual world. One famous version of possibilism is David Lewis's modal realism.
Most actualists will be happy to grant the interpretation of "I could go to the movies, or I could stay home" in terms of two distinct possible worlds. But they argue that the possibilist goes wrong in taking this as a sign that there exist other worlds that are just like ours, except for the fact that we are not actually in them. The actualist argues, instead, that when we claim "possible worlds" exist we are making claims that things exist in our own actual world which can serve as possible worlds for the interpretation of modal claims: that many ways the world could be (actually) exist, but not that any worlds which are those ways exist other than the actual, booming, buzzing world around us.
So, from this point of view, what distinguishes the actual world from other possible worlds is what distinguishes reality from a description of a simulation of reality, this world from Sherlock Holmes’: the former exists and is not a product of imagination and the latter does not exist and is a product of the imagination set in a modal construction.
From a modal realist’s point of view, such as Lewis’, the proposition "◊p" means that p obtains in at least one other, distinct world that is as real as the one we are in. If a state of affairs is possible, then it really obtains, it physically occurs in at least one world. Therefore, as Lewis is happy to admit, there is a world where someone named Sherlock Holmes lived at 221b Baker Street in Victorian times, there is another world where pigs fly, and there is even another world where both Sherlock Holmes exists and pigs fly.
This leaves open the question, of course, of what an actually existing "way the world could be" is; and on this question actualists are divided. One of the most popular solutions is to claim, as William Lycan and Robert Adams do, that "possible worlds" talk can be reduced to logical relations amongst consistent and maximally complete sets of propositions. "Consistent" here means that none of its propositions contradict one another (if they did, it would not be a possible description of the world); "maximally complete" means that the set covers every feature of the world. (More precisely: a set of propositions is "maximally complete" if, for any meaningful proposition P, P is either an element of the set, or the negation of an element of the set, or entailed by the conjunction of one or more elements of the set, or the negation of a proposition entailed by the conjunction of one or more elements of the set). Here the "possible world" which is said to be actual is actual in virtue of all its elements being true of the world around us.
Another common actualist account, advanced in different forms by Alvin Plantinga and David Armstrong views "possible worlds" not as descriptions of how the world might be (through a very large set of statements) but rather as a maximally complete state of affairs that covers every state of affairs which might obtain or not obtain. Here, the "possible world" which is said to be actual is actual in virtue of that state of affairs obtaining in the world around us. (Since it is maximally complete, only one such state of affairs could actually obtain; all the others would differ from the actual world in various large or small ways.)