DTS stands for Data Transformation Services. SSIS stands for SQL Server Integration Services. One of the main differences between these two things is time. The Data Transformation Service was the first system to be developed. Then the SQL Server Integration Services was developed. Both are used as a storage database for housing data.
Most likely you would use the SSIS because it is more up to date. DTS was part of the Microsoft SQL Server in 2000. SSIS didn’t come along until 2005 which is almost five years later. Also, SSIS can be used to take information from other sources, but DTS is used to take the information and put it into a database. However, they both have many similarities.