I believe classification is classifying records in a data set into predefined classes or even defining classes on the go. I look at it as pre-requisite for any valuable data mining, I like to think of it at unsupervised learning i.e. one does not know what he/she is looking for while mining the data and classification serves as a good starting point
Clustering on the other end falls under supervised learning i.e. one know what parameters to look for, the correlation between them along with critical levels. I believe it requires some understanding of statistics and maths
