The waterfall model is actually a step by step design procedure, frequently employed in software development processes, in which progress is viewed as moving gradually downwards (just like a waterfall) through the levels of Conception, Initiation, Analysis, Design, Construction, Testing, Production/Implementation and Maintenance.
The spiral model is actually a software development process incorporating features of both design and prototyping-in-stages, in order to unite benefits of top-down and bottom-up ideas. Also called the spiral lifecycle model or spiral development, it’s a systems development method (SDM) utilized in information technology (IT). The Spiral model brings together the characteristics of the prototyping model and the waterfall model. The spiral model is meant for big, pricey and sophisticated projects.