Difference between database and schema

A database is the main container, it contains the data and log files, and all the schemas within it. You always back up a database, it is a discrete unit on its own.

Schemas are like folders within a database, and are mainly used to group logical objects together, which leads to ease of setting permissions by schema.

EDIT for additional question

drop schema test1

Msg 3729, Level 16, State 1, Line 1
Cannot drop schema 'test1' because it is being referenced by object 'copyme'.

You cannot drop a schema when it is in use. You have to first remove all objects from the schema.

Related reading:

1. What good are SQL Server schemas?
2. MSDN: User-Schema Separation

Schema is a way of categorising the objects in a database. It can be useful if you have several applications share a single database and while there is some common set of data that all application accesses.

Database is like container of data with schema, and schemas is layout of the tables there data types, relations and stuff