What are the differences between a table variable, a temp table and a derived table?

A table variable just works like a static variable i.e. it scope lies within a certain block of execution whereas temp tables has a scope for the session unless it is dropped.
Table variables are recommended for holding very less data i.e. (10 KB) approx as it doesn't have statisctics build on it. So, it makes the performance of the query to be slow whereas temp tables are far beyond that. You can make its use whereever and whenever required but  its over usage creates problem with SGAM of tempdb and you will start seeing problem as 2:1:103.

Any update on this question?

As a brand new member, I suspect she has not got the "hang of things".  In other words, she does not realize that appropriate feedback can enhance or re-focus the question.