A President who has served two terms can run for any office other than President, and in many interpretations, Vice President.  Former Presidents can serve in Congress, but only two have:  John Quincy Adams served in the House and Andrew Johnson served in the Senate.

Over the past century, an unwritten rule has been that former Presidents should not speak out against the incumbent President or take an active role in domestic politics (outside of endorsements or fundraising during campaign years).  It’s a tradition or protocol that is meant to be respectful and well-intentioned in that former Presidents don’t want to make the current President’s job more difficult because they have personal knowledge of how difficult the Presidency truly is.  Unfortunately, it’s tough for us to see a leader like Bill Clinton on the sidelines when we know how capable and useful he might be if he only had a more active role.