Data migration
There is a difference between data migration and data integration activities. Data migration is a project by means of which data will be moved or copied from one environment to another, and removed or decommissioned in the source. During the migration (which can take place over months or even years), data can flow in multiple directions, and there may be multiple migrations taking place simultaneously. The ETL (extract, transform, load) actions will be necessary, although the means of achieving these may not be those traditionally associated with the ETL acronym.
Data processing
Data processing is, generally, "the collection and manipulation of items of data to produce meaningful information." 
In this sense it can be considered a subset of "information processing", "the change (processing) of information in any manner detectable by an observer." 
The term Data Processing (DP) has also been used to refer to a department within an organization responsible for the operation of data processing applications.