What is the difference between a schema and a table and a database?
A relation schema is the logical definition of a table - it defines what the name of the table is, and what the name and type of each column is. It's like a plan or a blueprint. A database schema is the collection of relation schemas for a whole database.
A table is a structure with a bunch of rows (aka "tuples"), each of which has the attributes defined by the schema. Tables might also have indexes on them to aid in looking up values on certain columns.
A database is, formally, any collection of data. In this context, the database would be a collection of tables. A DBMS (Database Management System) is the software (like MySQL, SQL Server, Oracle, etc) that manages and runs a database.
In a nutshell, a schema is the definition for the entire database, so it includes tables, views, stored procedures, indexes, primary and foreign keys, etc.