SQL Optimizer is a separate tool that can be purchased separately.It is also included in the Toad for Oracle Xpert Edition.
SQL Optimizer for Oracle automates the SQL optimization process and maximizes the performance of your SQL statements. SQL Optimizer analyzes, rewrites, and evaluates SQL statements located within database objects, files, or collections of SQL statements from Oracle's System Global Area (SGA). Once SQL Optimizer identifies problematic SQL statements, it optimizes the SQL and provides replacement code that includes the optimized statement.
SQL Optimizer also provides a complete index optimization and plan change analysis solution. It provides index recommendations for multiple SQL statements or a SQL workload, simulates index impact analysis, and generates SQL execution plan alternatives.
Auto optimizer is an option in Toad that is available in the Xpert Edition and higher.
Use Auto Optimize SQL to quickly optimize a single SQL statement. Toad searches for faster alternatives and allows you to compare them to the original statement and each other.
When searching for alternative rewrites, Toad may use several different methods to optimize the statement. For example, it may add a hint or change the SQL of the statement. The rewrites do not change the meaning of the query, but they do alter the execution plan.
In summary, SQL Optimizer has more advanced optimizing options and may be able to find an alternative even if Toad did not.