
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.

spiritual
Relating to the human spirit, the mind, or the soul; spiritual.
Nach dem Burnout suchte sie nach geistlicher und körperlicher Erholung.
After the burnout, she looked for spiritual and physical recovery.
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.
Christian
For songs, both christlich and geistlich can fit. Christlich refers to Christianity, while geistlich emphasizes religious or church use. A song for a church service is therefore usually geistlich, whereas a christliches Lied can also be sung outside that setting.

Das geistliche Lied ist für den gemeinsamen Gesang im Gottesdienst bestimmt.
The religious song is intended for everyone to sing together during the church service.
Das christliche Lied erzählt von Jesus, ist aber nicht für einen Gottesdienst bestimmt.
The Christian song tells the story of Jesus, but it is not intended for a church service.