
äußer
outer
Describes a position that is farther outside or on the periphery of something, as opposed to the inside or center.
Wir wohnen im äußeren Ring der Stadt, wo es ruhiger ist.
We live in the outer ring of the city, where it is quieter.
outer / external
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outer
Describes a position that is farther outside or on the periphery of something, as opposed to the inside or center.
Wir wohnen im äußeren Ring der Stadt, wo es ruhiger ist.
We live in the outer ring of the city, where it is quieter.

external / outward
Refers to the visible surface, appearance, or outward-facing aspects of a person or thing, as opposed to the inner nature or core.
Man sollte einen Menschen nicht nur nach seiner äußeren Erscheinung beurteilen.
You should not judge a person only by their outward appearance.
The adjective 'äußer-' (outer/external) is a comparative form derived from the adverb 'außen' (outside). It describes something that is located farther outside than something else.
Die äußere Schale der Nuss ist sehr hart.
The outer shell of the nut is very hard.
The adjective 'äußer-' (outer/external) is almost always used directly before a noun and must be declined. It normally does not stand alone at the end of a sentence.
Der äußere Eindruck kann täuschen.
The outward impression can be deceptive.
In its spatial meaning, 'äußer-' (outer) is often combined with nouns that describe a boundary or area, e.g. 'der äußere Rand' (the outer edge), 'die äußere Mauer' (the outer wall), or 'der äußere Stadtteil' (the outer district).
An der äußeren Grenze des Grundstücks steht ein Zaun.
There is a fence at the outer boundary of the property.
In the figurative sense, 'äußer-' (external/outward) often refers to appearance. Typical combinations are 'die äußere Erscheinung' (outward appearance), 'der äußere Schein' (outward appearance), or 'äußere Umstände' (external circumstances).
Lass dich nicht vom äußeren Schein blenden.
Do not let yourself be blinded by outward appearances.
external
Both words refer to something outside an inner area. äußer mainly describes a position on the outside or periphery, whereas extern emphasizes origin or affiliation outside a system or organization. äußer fits a position at the edge, while extern fits a provider from outside.

Wir wählten im Bus die äußeren Plätze nahe dem Fenster.
We chose the outer seats near the window on the bus.
Für das Projekt beauftragte die Firma einen externen Berater.
The company hired an external consultant for the project.