What is difference between application server and database server?

All your applications are installed in applications servers. Client machines can use these applications as if they were installed on their machines.

Database server is a computer porgram that provides database services to other programs or computers. Generally RDBMS OR ORDBMS installed in the server provide database server functionality. Client machines user front end tools or interface screen to interact with database servers.

The applications and database may reside in the same server or differet servers depending upon the requirement.