In a recent blog post, Forrester analyst Jonathan Penn talks about his conversation with fellow analyst Andras Cser on the two definitions that are floating around of Identity As A Service. They essentially agree with the assertion I made a few months ago (see my post "Defining Identity As A Service") that the standard definition should be the more general "identity management as an infrastructure SOA service".
The other definition floating around, which is narrower and more specific in scope, refers to the mechanism of providing managed identity management services in the classic SaaS model. This model is important in its own right as a different way of making identity management available to the market (especially SMB markets) in a more affordable, manageable manner. It should therefore have its own industry term that distinguishes it. I think Forrester's choice of Managed Identity Services (MIS) makes a lot of sense, as it is clear and already has some traction in the marketplace.