der Stapel
stack / pile
A quantity of things that are placed on top of one another, neatly or messily.
Auf seinem Schreibtisch liegt ein hoher Stapel Bücher.
There is a tall stack of books on his desk.

stack / pile
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stack / pile
A quantity of things that are placed on top of one another, neatly or messily.
Auf seinem Schreibtisch liegt ein hoher Stapel Bücher.
There is a tall stack of books on his desk.

The noun 'der Stapel' (the stack/pile) is closely related to the verb 'stapeln' (to stack), which means 'to place something neatly on top of something else'. When you stack things, a stack is formed.
Kannst du mir helfen, das Holz zu stapeln?
Can you help me stack the wood?
For physical objects, 'Stapel' (stack/pile) is often combined with things that can be placed on top of one another. Typical examples are 'ein Stapel Bücher' (a stack of books), 'ein Stapel Papier' (a stack of paper), or 'ein Stapel Kleidung' (a pile of clothes).
Neben dem Drucker liegt ein hoher Stapel Papier.
Next to the printer there is a tall stack of paper.
In a figurative sense, 'Stapel' (pile) is often used for a large number of tasks. Common combinations are 'ein Stapel Arbeit' (a pile of work) or 'ein Stapel Akten' (a stack of files) that still need to be processed.
Ich kann heute nicht kommen, ich habe noch einen riesigen Stapel Arbeit auf dem Schreibtisch.
I can't come today; I still have a huge pile of work on my desk.
The idiom 'vom Stapel laufen' (to be launched) is a fixed expression. It is used both literally for the launch of a ship and figuratively for the beginning of a new project.
Nächste Woche läuft unser neues Software-Produkt endlich vom Stapel.
Next week our new software product will finally be launched.
In computer science, 'der Stapel' (the stack) is a technical term for a specific data structure. In this context, the principle 'Last-In, First-Out' is often mentioned.
Der Prozessor legt die Adressen für die Rücksprünge auf dem Stapel ab.
The processor stores the addresses for the returns on the stack.
amount / crowd
'die Menge' and 'der Stapel' can both express that there is a lot of something. 'die Menge' only says that a certain or large quantity is present. 'der Stapel' fits when things are really lying on top of one another, for example books, paper, or clothing. In a figurative sense, people also say 'ein Stapel Arbeit' (a pile of work) when there is a lot of work. So 'Menge' is more general, while 'Stapel' makes the image more concrete or, with work, sounds a bit more figurative.

In der Bibliothek legt Tom einen Stapel Bücher auf den Tisch.
In the library, Tom puts a stack of books on the table.
Am Abend überrascht die Fahrerin die Menge an Gepäck im Bus.
In the evening, the driver is surprised by the amount of luggage on the bus.