ägyptisch
Egyptian
Refers to the country of Egypt, its population, its culture, or its language.
Die ägyptischen Pyramiden sind weltberühmt.
The Egyptian pyramids are world-famous.

Egyptian
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Egyptian
Refers to the country of Egypt, its population, its culture, or its language.
Die ägyptischen Pyramiden sind weltberühmt.
The Egyptian pyramids are world-famous.

The adjective 'ägyptisch' is derived from the country name 'Ägypten' (Egypt). The ending '-isch' is a very common way to form adjectives from geographical names.
Die italienische Küche ist weltberühmt.
Italian cuisine is world-famous.
Adjectives derived from geographical names with the ending '-isch' are written in lowercase in German. This is an important difference from English.
Wir haben eine Führung durch die ägyptische Abteilung des Museums gebucht.
We booked a guided tour through the Egyptian section of the museum.
The word 'ägyptisch' is very often used in connection with the history of ancient Egypt. Typical combinations are 'ägyptische Götter' (Egyptian gods), 'ägyptische Hieroglyphen' (Egyptian hieroglyphs), or 'die altägyptische Kultur' (ancient Egyptian culture).
In der Schule lernen wir gerade etwas über die ägyptischen Götter.
At school, we are currently learning about the Egyptian gods.
Arabic
'arabisch' and 'ägyptisch' can both have to do with language, people, and culture. 'arabisch' is broader: it fits the Arab world or the Arabic language in general. 'ägyptisch' is more specific and refers to Egypt, its people, culture, or language. Learners may confuse the words because Arabic is spoken in Egypt. But not everything Arab or Arabic is Egyptian, and 'ägyptisch' does not mean the whole Arab world.

Zu Hause kocht sie oft ägyptische Gerichte, weil ihr Mann aus Kairo kommt.
At home, she often cooks Egyptian dishes because her husband is from Cairo.
Im Gespräch sprach er aus Versehen von arabischer Musik, obwohl er nur Musik aus Ägypten meinte.
In the conversation, he accidentally spoke of Arab music, although he only meant music from Egypt.