There are clear difference between those two database integration modules. The Database Replicator is developed some years ago where the Database Connector is more recent.
The Database Replicator is used to duplicate data from an external database to you own database based on your own domain model. This is done with a background process to keep your data up-to-date from the external database. It's less ideal construction because data is duplicated in two different databases.
The Database Connector is an activity within the microflow to execute SQL statements (Read, Create, Update, Delete) which gives more control and flexibility. It gives the opportunity to work real-time with an external database without storing the data in the Mendix database. The replicator only retrieves data to the Mendix database.