innig
deep / heartfelt
Describes a very close, deep, and heartfelt emotional relationship or affection between people.
Die beiden verband eine innige Freundschaft, die ein Leben lang hielt.
The two shared a deep friendship that lasted a lifetime.

deep / heartfelt
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deep / heartfelt
Describes a very close, deep, and heartfelt emotional relationship or affection between people.
Die beiden verband eine innige Freundschaft, die ein Leben lang hielt.
The two shared a deep friendship that lasted a lifetime.

The adjective 'innig' (deep/heartfelt) is derived from 'innen' (inside). So it describes a feeling or relationship that comes from deep within, from the heart, and is not merely superficial.
Sie empfand eine innige Dankbarkeit für seine Hilfe.
She felt deep gratitude for his help.
When referring to relationships, 'innig' (deep/heartfelt) is often combined with nouns such as 'Liebe' (love), 'Freundschaft' (friendship), 'Beziehung' (relationship), or 'Umarmung' (hug). It always describes a very close and warm connection.
Zur Begrüßung gab es eine lange und innige Umarmung.
As a greeting, there was a long and heartfelt hug.
In the sense of a strong wish, 'innig' (deeply) can also be used as an adverb. It then intensifies verbs of hoping, wishing, or pleading, for example 'innig hoffen' (to hope deeply) or 'innig beten' (to pray fervently).
Er hoffte innig, die Prüfung bestanden zu haben.
He deeply hoped that he had passed the exam.
Especially with wishes, the superlative form 'innigste' (deepest) is often used. The phrase 'mein innigster Wunsch' (my deepest wish) expresses that this wish is the most important and deepest of all.
Ihr innigster Wunsch war es, einmal nach Japan zu reisen.
Her deepest wish was to travel to Japan one day.
narrow / close / tight
'eng' and 'innig' can both describe a very close relationship between people. 'eng' is more general and can also sound more matter-of-fact, for example with friends, family, or collaboration. 'innig' is stronger and more emotional. It means deep, heartfelt affection. In everyday language, people often say 'eine enge Freundschaft' (a close friendship). 'innig' fits better when you want to emphasize the special warmth and depth of a relationship.

Mila hat eine innige Beziehung zu ihrer Großmutter.
Mila has a deep bond with her grandmother.
Seit der Schulzeit haben Lena und Sofia eine enge Freundschaft.
Lena and Sofia have had a close friendship since their school days.