die Marke
brand
A name or symbol that identifies a product or service from a particular company; a branded product.
Adidas ist eine weltweit bekannte Marke für Sportbekleidung.
Adidas is a globally known brand for sportswear.

brand / mark / stamp
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brand
A name or symbol that identifies a product or service from a particular company; a branded product.
Adidas ist eine weltweit bekannte Marke für Sportbekleidung.
Adidas is a globally known brand for sportswear.

'Die Marke' is related to the verb 'markieren' (to mark). All meanings have to do with the basic idea of a sign, label, or marking.
Der Wanderweg ist mit roten Marken an den Bäumen markiert.
The hiking trail is marked with red markers on the trees.
In the context of products and consumption, typical collocations are 'eine bekannte Marke' (a well-known brand), 'einer Marke treu sein' (to be loyal to a brand), 'Markenkleidung tragen' (to wear branded clothing), or 'eine Marke schützen lassen' (to have a brand protected).
Viele Jugendliche tragen gerne Kleidung von bekannten Marken.
Many teenagers like to wear clothing from well-known brands.
When it comes to records or levels, 'Marke' is often used with verbs such as 'erreichen' (to reach), 'knacken' (to break), 'überschreiten' (to exceed), or 'unterbieten' (to go below). The combination 'eine magische Marke' (a magical mark) is also common.
Der Aktienindex hat die Marke von 15.000 Punkten überschritten.
The stock index has exceeded the mark of 15,000 points.
If the conversation or text is about the post office, letters, or postcards, 'Marke' almost always means a postage stamp. It is a common abbreviation.
Ich muss zur Post gehen und ein paar Marken kaufen.
I have to go to the post office and buy a few stamps.
In the context of supermarkets and shopping carts, 'Marke' refers to the small chip or coin you need for the cart. Sometimes the word 'Chip' is also used.
Ich habe keine Münze, hast du eine Marke für den Einkaufswagen?
I don't have a coin; do you have a token for the shopping cart?
company / firm
'die Firma' and 'die Marke' are often connected, but they do not mean the same thing. A 'Firma' is the company, or also the official name of a company. A 'Marke' is the name or symbol under which a product or service is known. They are easy to confuse because one company can have one or more brands. If you are talking about the manufacturer or employer, 'Firma' fits. If you are talking about the name on the product or the well-known symbol, 'Marke' fits.

Beim Kauf der Schuhe achtet du nicht nur auf die Marke, sondern auch auf den Preis.
When buying the shoes, you pay attention not only to the brand, but also to the price.
Zu Hause suche ich die Telefonnummer der Firma, die den Kühlschrank geliefert hat.
At home, I look up the phone number of the company that delivered the refrigerator.