die Münze
coin
A flat, usually round piece of metal that has been minted as official means of payment.
Ich habe keine passende Münze für den Parkautomaten.
I don't have the right coin for the parking meter.

coin / mint
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coin
A flat, usually round piece of metal that has been minted as official means of payment.
Ich habe keine passende Münze für den Parkautomaten.
I don't have the right coin for the parking meter.

The idiom 'etwas für bare Münze nehmen' means to believe something immediately without questioning it. 'Bar' here means 'genuine' or 'pure'.
Das war nur ein Scherz, du solltest nicht alles für bare Münze nehmen.
That was just a joke; you shouldn't take everything at face value.
In everyday use as a means of payment, 'Münze' (coin) is often used with verbs such as 'einwerfen' (to insert, into a machine), 'sammeln' (to collect), or 'wechseln' (to change/exchange).
Ich muss noch Geld wechseln, um eine passende Münze für den Einkaufswagen zu haben.
I still need to change some money so I have the right coin for the shopping cart.
When referring to a medal or collector's item, 'Münze' (coin) is often combined with words like 'Gedenk-' (commemorative), 'Sonder-' (special), or 'Jubiläums-' (anniversary). Verbs like 'prägen' (to mint) or 'herausgeben' (to issue) also point to this meaning.
Zum 200. Geburtstag des Dichters wurde eine Gedenkmünze geprägt.
A commemorative coin was minted for the poet's 200th birthday.
In the rare meaning of the minting facility, 'Münze' (mint) almost always appears with the preposition 'in' and often with a place name. It then refers to the building where money is produced.
Diese seltene Münze wurde in der Münze Berlin hergestellt.
This rare coin was produced at the Berlin Mint.
medal / order
'die Münze' and 'der Orden' can both be a piece of metal that has a special meaning. In this overlap, it is not about 'Münze' as money, but about a commemorative coin or keepsake. An 'Orden', by contrast, is clearly an award for special achievements or service and is given by a state or an organization. Learners may confuse the words because both can sometimes look ceremonial and be collected. If it is about an award for an achievement, 'Orden' is more precise. If it is more of a minted metal keepsake, 'Münze' fits.

Zum Stadtjubiläum bekam jeder Gast eine besondere Münze.
For the city's anniversary, every guest received a special commemorative coin.
Der Feuerwehrmann erhielt einen Orden für seinen mutigen Einsatz.
The firefighter received a medal for his brave service.