For DB2, schema is used as namespaces. So if you want to uniquely identify an object in a database you would say *schema.object_name*. This is a very handy way to achieve multitenancy. You can have a separate schema for each tenant in your database. This provides for good separation of concerns from both security as well as management aspects. You can have 32K schemas in a single DB2 database.
A catalog in DB2 is simply a collection of system tables that contain metadata about the database. In general, it is considered a bad practice to access catalog objects directly. It is best to use the facilities provided by your API (e.g. JDBC) to explore the catalog and the metadata it contains.
DB2 also has other abstraction layers. You can have multiple instances of DB2 running on the same machine. Each instance can manage 256 separate databases (each with 32K schemas). The number of DB2 instances on a server is limited only by the amount of memory you have available. At one point in time we had 120 instances of DB2 (each with one database and 10 connections) running on Amazon EC2 m1.large.
You can also have multiple installs of DB2 on a single server. it is useful when testing a new version you plan to migrate to. I do find it confusing though often forgetting to switch to the right install.