On a very basic level, a DBMS is a method for looking at something. For ex. SQL Server, MySQL, and others. It is basically a program that lets you communicate with databases.
Database management system is a product which sorts out information in a database, gets information, controls and manipulates information. Generally, most of DBMS like SQL Server Management Studio or MySQL Workbench provides an easy to use interface. Also, it lets the user extract data, database entities and structures at will with simple mouse clicks.
AN ERP is a product which oversees the complex business process and incorporates each one of the segments of different modules and runs at a real time. It can involve a solitary database or collections of DBMS. There can be a database administrator who might use an IDE like SQL Server Management Studio. Another front end user who enters data into sales dashboard will have an altogether different screen.
The user base of DBMS is of specialized Users like Database administrators, developers, testers and others. But in comparison to an ERP, the user base can range from skilled to normal users.