The difference is that Lytro actually does it, instead of simulating it.
It'd be fun to play around with the software to see in which cases it breaks (perhaps taking a photo of a framed landscape photo with another landscape behind, for example)
Lytro is also "just" simulating it, but with slightly more/different data. They capture a light field but that doesn't magically give them depth values; they have to estimate them using an optimization, and then render the final image using a very similar algorithm.
In reality the Lytro has abysmal performance, which questions the value of lightfield technology as a whole.
Instead of capturing the 'light field' you may as well capture most of the image.
Secondly the loss of the 2nd derivative of the k-vector makes lightfield currently unsuitable for use in a microscope (although they are working on it...). Although there might be better techniques for refocusing, such as division in the spatial frequency domain.
It'd be fun to play around with the software to see in which cases it breaks (perhaps taking a photo of a framed landscape photo with another landscape behind, for example)