I'm not an expert for the Spiral Model, but from the wikipedia-definition, it seems to me that there are some significant differences.
For example, in an Agile project, at the end of an iteration doesn't stand a prototype, but a fully functional, fully tested, potentially deployable (1) system, containing the highest priority features on the feature list.
The requirements gathering at the start of the project is meant to be just barely enough to get going (to take the next step) and are meant the be fleshed out just shortly before they get actually implemented. Changes are to the requirements are welcomed.
Also, there is much more to Agile than just doing iterative development - a focus on faces to face conversation instead of written communication, a focus on bringing business people and technical together in their day-to-day work. A focus in collaboratively maximizing value instead of defining and then fulfilling a contract.
In case you didn't see it yet, take a look at the Agile Manifesto, which basically is the definition for Agile Software Development.
(1) That doesn't mean that it has to make business sense to deploy the system, "just" that it is technically feasible. It should be a pure business decision whether to deploy the system at the end of an iteration.