The basic difference, as I see it, is that most Spiral models of development still insist on big, up-front design. The emphasis is on knowing as much as you can about how the system will be used; discovering all the use cases. Once you know these, then you design the system and break it down into phases that follow an iterative detail-design, implementation, test, refactor-design loop. In Agile, their is some up-front planning -- perhaps gathering large grain understanding (story titles) -- so that reasonable releases can be described, but each release is planned independently and we delay discovery of the details until we are ready to begin implementation of that release. We expect change and don't try to know everything first.
Another thing that differs is that most Agile philosophies involve "test-first" methods. This is different from spiral where testing is often an activity unto itself and tests are not developed prior to code. Most often they are planned in advance, but developed in parallel or after coding. Many agile methods insist on developing tests first as the specification for the code.
They are similar in that they are iterative. They differ in the implementation and understanding of what an iteration is.
