In a sense, Deleuze's virtual and Lewis's possible worlds compete to provide the "right" conception of the possible. The descriptions are indeed similar but this is deceptive, Deleuze and Lewis, in part reflecting their respective traditions (continental and analytic), are far apart on the possible because they are far apart on the real. Lewis's "real" is closer to Deleuze's "actualized" (and then perhaps desiccated).
Here is how Deleuze characterizes the virtual in Difference and Repetition:
"The virtual is opposed not to the real but to the actual. The virtual is fully real in so far as it is virtual. Exactly what Proust said of states of resonance must be said of the virtual: “Real without being actual, ideal without being abstract”; and symbolic without being fictional. Indeed, the virtual must be defined as strictly a part of the object – as though the object had one part of itself in the virtual into which it plunged as though into an objective dimension."
Deleuze's virtual is not the kind of impotent possible that has existence added to it later on, it is an active "virtual field" that causes actual experience to happen. Peirce had a similar view of possibility, his "real possibilia", as-if real, living breathing real, albeit not actualized, and used "virtual" in a somewhat similar sense:"A virtual X (where X is a common noun) is something, not an X, which has the efficiency (virtus) of an X", Peirce wrote. He in turn was elaborating what was "implicit" in Duns Scotus. Of course, Deleuze moved the notion far from its historical roots but it is still closer to them than Lewis is. For more on this relation see Kiryushchenko's The Idea of Virtuality in Peirce's Semiotics and Deleuze's Transcendental Empiricism:
"In his Organs without Bodies: on Deleuze and Consequences (2004) Slavoj Žižek calls Gilles Deleuze “the philosopher of the Virtual”, adding that “what matters to Deleuze is not virtual reality, but the reality of the virtual” . This change in word order is important. It marks a decisive shift from the idea of the virtual as an imitation of reality to the more historically correct ontological understanding of the virtual as revealing the fundamental metaphysical properties common to the world of human conventions and to the universe at large."
Today, with the ubiquity of possible worlds, it is hard to appreciate that the original, Aristotelian, notion of the possible was different. His potential, "matter", was real enough, but still required the entelechy, actualization. For Aristotle, the virtual is the multitude of potentialities circumscribed by the essential, some potentialities are allowed while others are not, because they would break the essence. Aquinas even used virtual and potential synonymously.
Deleuze's virtual derives from Aristotelian potential, not from Leibniz's possible worlds. This is the difference between (possible) becoming and (possible) being (real vs actual), static and dynamic, analytic and poetic, intensional and extensional (ideal vs abstract). Here is Felt's illuminating contrast from Impossible Worlds:
"For whether with Lewis one takes possible worlds to be as real as the actual, or one tries to replace them solely by the actual, the upshot seems the same: all is reduced to a planar understanding of what it means to be. In these controversies the anti-Parmenidean (Aristotelian) notion of potentiality, as an intrinsic character of the actual, has tended to be supplanted by possibilities (in the plural), Lewis’s “ways things could have been,” purely formal and discrete patterns. The dynamism of potentiality has been exchanged for a dust of homeless forms."
It is only in scholastic times that we see the modern conception of modal patterns, possible worlds, starting to emerge. The crucial step was taken perhaps by Molina, who introduced the notion of "counterfactuals of freedom",
what creatures would have freely chosen to do if things had been different. It was left to Leibniz to assemble these dry-frozen how-things-could-bes into possible worlds, filled with outcomes of acting but without the acting. But of course the idea only fully triumphed after post-Cantorian extensionalization of logic and mathematics, extended to modal logic and philosophy by Kripke in 1950-s. Lewis belongs to this Leibnizian tradition.