die Mauer
wall
A solid structure, usually made of stone, brick, or concrete, that serves as a boundary, support, or part of a building.
Um den Garten wurde eine hohe Mauer gebaut.
A high wall was built around the garden.

wall
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wall
A solid structure, usually made of stone, brick, or concrete, that serves as a boundary, support, or part of a building.
Um den Garten wurde eine hohe Mauer gebaut.
A high wall was built around the garden.

The related verb is 'mauern'. Literally, it means to build a wall. Colloquially, it is also used when someone blocks, gives no information, or refuses to cooperate.
Der Verdächtige mauerte bei der Befragung durch die Polizei.
The suspect stonewalled during police questioning.
With a physical wall, prepositions show different relationships. 'An der Mauer' (at/on the wall; dative) describes a position, while 'gegen die Mauer' (against/into the wall; accusative) expresses movement or impact.
Das Fahrrad lehnte an der Mauer.
The bicycle was leaning against the wall.
When 'die Mauer' (the Wall) is used in a historical German context, it almost always refers to the Berlin Wall. Typical signal words are 'Fall' (fall), 'Bau' (construction), 'DDR' (GDR), or years such as 1961 and 1989.
Viele Familien wurden durch den Bau der Mauer getrennt.
Many families were separated by the construction of the Wall.
In the figurative meaning, 'Mauer' (wall) describes an invisible barrier between people. It is often combined with abstract nouns like 'Schweigen' (silence), 'Ablehnung' (rejection), or 'Ignoranz' (ignorance), usually in the form 'Mauer des/der ...' (wall of ...).
Sein Vorschlag stieß im Team auf eine Mauer der Ablehnung.
His suggestion ran into a wall of rejection within the team.
border / limit
'die Grenze' and 'die Mauer' can both separate things. But a 'Grenze' is primarily a line or a limit. It can be political, geographical, or also figurative. A 'Mauer' is a real structure made of stone, concrete, or similar material. It can make a border visible, but not every border is a wall. In a figurative sense, a 'Mauer' can also arise between people when no one speaks openly. Learners may confuse the words because both have to do with separation. If you mean a line or a limit, 'Grenze' fits. If you mean a solid obstacle, 'Mauer' fits.

Hinter dem Garten steht eine hohe Mauer aus rotem Stein.
Behind the garden stands a high wall made of red stone.
Die Grenze zwischen den beiden Ländern verläuft durch den Wald.
The border between the two countries runs through the forest.