Data Profiling, also referred to as Data Archeology is the process of assessing the data values in a given dataset for uniqueness, consistency and logic. Data profiling cannot identify any incorrect or inaccurate data but can detect only business rules violations or anomalies. The main purpose of data profiling is to find out if the existing data can be used for various other purposes.
Data Mining refers to the analysis of datasets to find relationships that have not been discovered earlier. It focusses on sequenced discoveries or identifying dependencies, bulk analysis, finding various types of attributes, etc.