Right-to-work and at-will are frequently confused, but they address entirely different aspects of employment law.
At-will employment means you can be fired without cause (subject to illegal discrimination/retaliation exceptions).
Right-to-work means you cannot be required to join a union or pay union dues as a condition of employment. It has NOTHING to do with whether you can be fired.
A state can be both at-will AND right-to-work (like Texas and Florida), or at-will but NOT right-to-work (like California and New York).
When people say "I live in a right-to-work state so I can be fired for anything" — they're confusing two different concepts. The protections against discriminatory or retaliatory firing exist regardless of right-to-work status.
Sources: National Labor Relations Act, Section 14(b) (29 U.S.C. § 164(b)) (right-to-work); at-will employment is a common-law doctrine, not a federal statute.