geistig
mental
Relates to a person's mind, thinking, and intelligence.
Lesen und Rätsel lösen sind gute Übungen für die geistige Fitness.
Reading and solving puzzles are good exercises for mental fitness.

mental / spiritual
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mental
Relates to a person's mind, thinking, and intelligence.
Lesen und Rätsel lösen sind gute Übungen für die geistige Fitness.
Reading and solving puzzles are good exercises for mental fitness.

The adjective 'geistig' derives directly from the noun 'der Geist' (mind/spirit). The different meanings of 'geistig' reflect the different meanings of 'Geist': mind, soul, or even alcohol.
Er hat einen wachen Geist und ist sehr neugierig.
He has an alert mind and is very curious.
You can tell from context whether 'geistig' refers to the mind (m01) or the soul/spirit (m02). Nouns like 'Arbeit' (work), 'Leistung' (performance), or 'Behinderung' (disability) point to the mind, while 'Haltung' (attitude), 'Wachstum' (growth), or 'Ebene' (level/plane) point to the spiritual meaning.
Eine geistige Behinderung beeinflusst die kognitiven Fähigkeiten.
An intellectual disability affects cognitive abilities.
In connection with the mind, 'geistig' is often combined with nouns that describe abilities or states. Typical examples are: 'geistige Arbeit' (mental work), 'geistiges Eigentum' (intellectual property), or 'eine geistige Anforderung' (a mental requirement/challenge).
Die Erfindung ist sein geistiges Eigentum.
The invention is his intellectual property.
The meaning 'alkoholisch' (alcoholic) is used almost exclusively in the fixed and formal expression 'geistige Getränke' (alcoholic beverages). You often find it in laws, official documents, or in gastronomy.
Auf der Weinkarte standen auch diverse geistige Getränke.
The wine list also included various alcoholic beverages.
inner
'inner' and 'geistig' can both describe something that is not physical or visible. 'inner' fits more with feelings, personal thoughts, and one's own experience, for example with calm, fear, or a conflict. 'geistig' is used more when the topic is thinking, intellect, concentration, or mental abilities. The words can be confused because both involve what is in the head or within the person. As a guide: with feelings, 'inner' sounds more natural; with thinking and the intellect, 'geistig' does.

Nach acht Stunden Arbeit war Max geistig sehr müde.
After eight hours of work, Max was mentally very tired.
Nach dem Streit spürte sie eine innere Unruhe.
After the argument, she felt an inner restlessness.