Agile is spiral. Totally. In part, the name was changed for marketing purposes.
The problem is that spiral tends to imply "big design up front" -- where you plan out many spirals, each in order of risk. Spiral, however, isn't Agile -- it's just incremental execution in order of risk.
One big distinction that Agile adds is the "don't overplan things you can't know yet."
Agile is spiral, but you create detailed plans for just one increment at a time.
Agile adds a lot of other things, also. Spiral is a very technical approach. Agile, however, recognizes that technology is built by people. The Agile Manifesto has four principles that are above and beyond the Boehm's simple risk management approach.
