geistlich
clerical / religious
Relating to the church, a religion, or the clergy.
Der Bischof ist das geistliche Oberhaupt der Diözese.
The bishop is the spiritual head of the diocese.

spiritual / clerical
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clerical / religious
Relating to the church, a religion, or the clergy.
Der Bischof ist das geistliche Oberhaupt der Diözese.
The bishop is the spiritual head of the diocese.

The adjective 'geistlich' (spiritual/clerical) is derived from the noun 'der Geist' (the spirit/mind). This connection helps you understand both meanings: the religious one (relating to the Holy Spirit) and the spiritual one (relating to the human spirit).
Viele Menschen suchen in der Meditation eine Form von geistlicher Erfahrung.
Many people seek a form of spiritual experience in meditation.
You can recognize the religious meaning from the context. If the topic is the church, offices, hymns, or ceremonies, this meaning is almost always intended.
Die Orgel spielte geistliche Musik von Bach.
The organ played sacred music by Bach.
In a church context, 'geistlich' (clerical/religious) is often combined with certain nouns. Typical examples are 'geistliche Lieder' (religious hymns), 'geistliche Musik' (sacred music), 'ein geistliches Oberhaupt' (a spiritual head), or 'ein geistliches Amt' (a clerical office).
Der Chor sang auf der Hochzeit ein geistliches Lied.
The choir sang a religious hymn at the wedding.
You can recognize the spiritual meaning from words that refer to a person's condition or development. These include terms such as 'Gesundheit' (health), 'Wohlbefinden' (well-being), 'Erneuerung' (renewal), or 'Zustand' (state).
Yoga soll das geistliche Gleichgewicht fördern.
Yoga is meant to promote spiritual balance.
religious
'religiös' and 'geistlich' can both have to do with faith and religion. 'religiös' is the normal, broad word for faith, religion, or religious topics. 'geistlich' sounds more specific and is often used for things connected with the church, the clergy, or inner spiritual life, for example 'ein geistliches Lied' (a religious/spiritual song) or 'ein geistlicher Rat' (spiritual advice). The words can be confused because both appear in religious contexts. In everyday language, 'religiös' is usually simpler and more general; 'geistlich' fits more in church-related or spiritual contexts.

Der Chor singt am Abend ein geistliches Lied.
In the evening, the choir sings a religious song.
Im Unterricht sprechen wir über religiöse Feste in verschiedenen Ländern.
In class, we talk about religious festivals in different countries.