Data Conversion and Data Migration are used interchangeably. However, I consider Data Conversion is a subset of Data Migration1. Data Conversion is the activities of extracting data from the source, transforming the data and loading it to the target system based on a set of requirements. Data Migration on the other hand involves Data Conversion activities in addition to all the activities required to move the application successfully to utilize the target data. This will include data profiling, data cleansing, data exception mitigation and validating that the application side to make sure it works with the converted data and may also involve creating ongoing data quality process on the target system. So, with a Data Migration projects, it is conceivable that the Data Conversion portion of the Data Migration is successful in moving the data to the target system based on the requirements and yet the Data Migration project has failed miserably because the applications were not able to work with such data.
Both terms are used interchangeably in many of industry internet papers I looked at. The important thing is to understand are the activities involved to a successful Data Migration\Data Conversion project. There are very rare situations when a company has to convert data without using it in some manner. However, projects do tend to separate the two and focus on the application part of the project with less emphasis on the data conversion activities I defined above.
1 Projects that are considered Data Integration have a component that may deal with converting data (Data Conversion).