der Mantel
coat
A long item of clothing worn over normal clothes to protect oneself from cold or rain.
Zieh dir einen Mantel an, es ist kalt draußen!
Put on a coat; it's cold outside!

coat
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coat
A long item of clothing worn over normal clothes to protect oneself from cold or rain.
Zieh dir einen Mantel an, es ist kalt draußen!
Put on a coat; it's cold outside!

When 'Mantel' (coat) is an item of clothing, it is often used with the verbs 'anziehen' (to put on), 'ausziehen' (to take off), or 'tragen' (to wear).
Er zog seinen Mantel aus und hängte ihn an die Garderobe.
He took off his coat and hung it on the coat rack.
The meaning 'Hülle' (covering) or 'Schicht' (layer) can be recognized from the context. It is usually used for technical or scientific objects, such as 'Reifenmantel' (tire casing) or 'Erdmantel' (Earth's mantle).
Der äußere Mantel des Kabels schützt die inneren Drähte.
The outer covering of the cable protects the inner wires.
The expression 'den Mantel des Schweigens' (the cloak of silence) is usually combined with the verb 'breiten' (to spread) or 'hüllen' (to wrap). The thing being kept silent about is introduced with the preposition 'über' + accusative.
Über die wahren Gründe wurde der Mantel des Schweigens gebreitet.
A cloak of silence was spread over the real reasons.
jacket
'die Jacke' and 'der Mantel' are both items of clothing with sleeves that you wear over other clothes, often against cold, wind, or rain. The most important difference is the length, and often also the style. A jacket is usually shorter and ends around the hips or waist. A coat is longer and often reaches the thighs, knees, or even lower. Learners may confuse the words because both are worn outside. For everyday life, sports, or in-between weather, people often say 'Jacke'; for a long, warmer, or more elegant item of clothing, 'Mantel' is more precise.

Am Morgen hängt Herr Schneider seinen langen Mantel an die Garderobe.
In the morning, Mr. Schneider hangs his long coat on the coat rack.
Bei dem Wind nimmt Lisa lieber ihre warme Jacke mit.
With this wind, Lisa would rather take her warm jacket with her.