Refactoring, as talked about in Martin Fowler's book and by people who've done academic work on the subject, consists of changes that alter the structure of code while preserving functionality.
In many environments, specific refactorings are pre-packaged, such that they know their preconditions for working properly, and work with almost mathematical precision. In these sorts of environments, with additional support like Unit Tests, you gradually morph from one structuring of the system into another. This can be a lot safer than "ripping out the plumbing and throwing the bigger pieces back together." (I've also done the rip/reassemble thing. It's often fun and yields good results too.)
In many environments, specific refactorings are pre-packaged, such that they know their preconditions for working properly, and work with almost mathematical precision. In these sorts of environments, with additional support like Unit Tests, you gradually morph from one structuring of the system into another. This can be a lot safer than "ripping out the plumbing and throwing the bigger pieces back together." (I've also done the rip/reassemble thing. It's often fun and yields good results too.)