In our review, we explore two different flavors of social norms: strength and stability. These two fundamental features are crucial for understanding norm change and designing effective interventions. Strong norms, which significantly influence behavior and are widely adopted, and stable norms, which endure over time, are essential for group coordination and addressing collective challenges. Using game theory, we discuss what constitutes norms' strength, drawing on Bicchieri's framework and tightness-looseness theory. Using the game-theoretic notion of evolutionary stable states, we also differentiate between strength and stability, listing possible enforcement mechanisms like punishment, gossip, and perceived legitimacy. Here we argue that stability is not a mere consequence of strength but a different feature of norms that is separate but linked. We conclude by highlighting the need for a theoretical definition of stability, incorporating various mechanisms from the literature to provide a robust theoretical framework for future research on social norms.