der Schwarm
swarm
A large group of animals, especially insects, birds, or fish, that move together.
Ein riesiger Schwarm Stare verdunkelte für einen Moment den Himmel.
A huge swarm of starlings darkened the sky for a moment.

swarm / crush
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swarm
A large group of animals, especially insects, birds, or fish, that move together.
Ein riesiger Schwarm Stare verdunkelte für einen Moment den Himmel.
A huge swarm of starlings darkened the sky for a moment.

The noun 'der Schwarm' is connected with the verb 'schwärmen'. Birds or bees 'schwärmen aus' (swarm out), and you can also 'für jemanden schwärmen' (to have a crush on someone) when you are in love. This connection explains the different meanings.
Als Kind habe ich für einen berühmten Sänger geschwärmt.
As a child, I had a crush on a famous singer.
In the animal world, 'Schwarm' is used for certain groups. Typical examples are 'ein Schwarm Fische' (a school of fish), 'ein Schwarm Vögel' (a flock/swarm of birds, especially starlings), 'ein Schwarm Bienen' (a swarm of bees), or 'ein Schwarm Mücken' (a swarm of mosquitoes).
Beim Tauchen sahen wir einen bunten Schwarm Fische.
While diving, we saw a colorful school of fish.
When 'Schwarm' describes a person one is in love with, it is often used with a possessive pronoun (mein, dein, ...) or in the phrase 'einen Schwarm haben für' (to have a crush on). This meaning is colloquial.
Sie hat ihrem besten Freund nie erzählt, dass er ihr heimlicher Schwarm war.
She never told her best friend that he was her secret crush.
The use of 'Schwarm' for a crowd of people is a metaphor. It describes a large, dense group of people moving like a swarm of animals, often without a clear individual goal.
Ein Schwarm von Neugierigen hatte sich an der Unfallstelle versammelt.
A swarm of curious onlookers had gathered at the accident site.
amount / crowd
'die Menge' and 'der Schwarm' can both describe a large group. 'die Menge' is general and neutral: it can refer to things, people, or substances. 'der Schwarm' is especially used for animals that move together, for example birds, fish, or insects. Figuratively, it can also mean a dense group of people moving in a similar way. Learners may confuse the words because both can be used for many people. But 'Schwarm' emphasizes movement and cohesion; 'Menge' only says that there are many.

Über dem See fliegt ein Schwarm Vögel in Richtung Wald.
A flock of birds is flying over the lake toward the forest.
Meine Nachbarin gibt der Menge vor dem Haus ruhig Auskunft.
My neighbor calmly gives information to the crowd in front of the house.