Mur vs. muraille
In French, both mur and muraille translate to "wall" in English. However, they are not interchangeable. The choice between them depends on the size, scale, and function of the wall in question.
Mur
A1Mur is the general, everyday term for a wall. It can refer to the interior or exterior walls of a building, a garden wall, or even a figurative barrier. It is the most common and versatile word for "wall".
J'ai accroché un nouveau tableau au mur du salon.
(I hung a new painting on the living room wall.)
Le chat aime se promener sur le petit mur du jardin.
(The cat likes to walk on the little garden wall.)
La peinture du mur extérieur de la maison s'écaille.
(The paint on the exterior wall of the house is peeling.)
Un mur anti-bruit a été construit le long de l'autoroute.
(A sound barrier wall was built along the highway.)
Il y a un mur d'incompréhension entre eux.
(There is a wall of misunderstanding between them.)
Muraille
B1Muraille refers to a very large, thick, and imposing wall, typically an ancient or defensive one. Think of the walls surrounding a medieval city, a fortress, or a castle. It carries a connotation of grandeur, history, and massive scale.
Nous avons visité les murailles de la vieille ville de Dubrovnik.
(We visited the walls of the old city of Dubrovnik.)
Les soldats se tenaient au sommet de la muraille du château.
(The soldiers stood at the top of the castle wall.)
La Grande Muraille de Chine est visible depuis l'espace.
(The Great Wall of China is visible from space.)
La falaise se dresse devant nous comme une muraille infranchissable.
(The cliff rises before us like an impassable wall.)
Le journaliste s'est heurté à une muraille de silence de la part du gouvernement.
(The journalist was met with a wall of silence from the government.)
Summary
In essence, a mur is any standard wall you would encounter in daily life, such as one in a house or garden. A muraille is a much larger, more formidable wall, almost always with a historical or defensive purpose, like the ramparts of a city or a fortress. If you can walk on top of it and it surrounds a city, it's a muraille.