elterlich
parental
Relates to the parents, comes from the parents, or is characteristic of them.
Er wohnt immer noch im elterlichen Haus.
He still lives in his parents' house.

parental
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parental
Relates to the parents, comes from the parents, or is characteristic of them.
Er wohnt immer noch im elterlichen Haus.
He still lives in his parents' house.

The adjective 'elterlich' (parental) is derived directly from the noun 'die Eltern' (the parents). The ending '-lich' turns the noun into an adjective meaning 'like parents' or 'coming from the parents'.
Sie schätzt den elterlichen Rat sehr.
She values parental advice very much.
In this meaning, 'elterlich' (parental) is almost always connected with possession or legal concepts. The most common collocation is 'das elterliche Haus' (the parental home / one's parents' house). Others are 'die elterliche Wohnung' (the parents' apartment) or 'die elterliche Sorge' (custody).
Für die Reise brauchte der Minderjährige die elterliche Zustimmung.
For the trip, the minor needed parental consent.
When it is about behavior, 'elterlich' (parental) is combined with abstract nouns. Typical examples are 'elterliche Fürsorge' (parental care), 'elterliche Strenge' (parental strictness), or an 'elterlicher Blick' (parental look).
Mit einer Mischung aus elterlicher Wärme und Strenge erzog sie ihre Kinder.
She raised her children with a mixture of parental warmth and strictness.
familial / familiar
'familiär' and 'elterlich' can both have to do with family and closeness. However, 'familiär' is broader: it can refer to the family in general or describe a warm, personal atmosphere. 'elterlich' refers more specifically to parents or to behavior that is typical of parents, for example care or authority. Learners may confuse the words because parents are part of the family. When it is about the whole family or a warm atmosphere, 'familiär' fits better. When it is directly about a mother, a father, or parent-like care, 'elterlich' is more precise.

Noah braucht vor der Prüfung noch etwas elterliche Unterstützung.
Noah still needs some parental support before the exam.
In dem kleinen Hotel war die Atmosphäre sehr familiär.
In the small hotel, the atmosphere was very warm and family-like.