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inwardly
Refers to a person's world of feelings and thoughts; emotional or mental. It describes states that are not necessarily visible from the outside.
Obwohl sie lächelte, war sie innerlich sehr nervös.
Although she was smiling, inwardly she was very nervous.
The word 'innerlich' (inner/inwardly) is derived from 'innen' (inside). The ending '-lich' makes it an adjective. So it describes how something is 'innen' (inside).
Bitte warte drinnen, es ist zu kalt draußen.
Please wait inside; it's too cold outside.
When it comes to feelings, 'innerlich' (inwardly) describes a state that you do not necessarily show outwardly. It is often used as an adverb to modify verbs like 'lachen' (to laugh), 'weinen' (to cry), or 'aufgeben' (to give up).
Er hat den Job schon innerlich aufgegeben.
He has already given up on the job inwardly.
In a medical context, 'innerlich' (internal) signals that a medication is intended to be taken internally, e.g. swallowed. It often stands in contrast to 'äußerlich' (external, for the skin).
Diese Tropfen sind zur innerlichen Einnahme bestimmt.
These drops are intended for internal use.
In connection with organizations or groups, 'innerlich' (internal) often describes problems or structures. Typical combinations are 'innerliche Konflikte' (internal conflicts), 'innerliche Zerrissenheit' (inner turmoil), or 'innerliche Erneuerung' (internal renewal).
Die innerlichen Konflikte haben die Partei geschwächt.
The internal conflicts weakened the party.
inside
'innen' and 'innerlich' both have to do with the inside, but they are used differently. 'innen' usually describes a place or direction within a room, building, or object. 'innerlich' is more likely to describe something you cannot directly see: feelings and thoughts, or something inside the body. Learners confuse the words because both seem like the opposite of 'außen' (outside). For a concrete place, you say 'innen'. For feelings or processes in the body, you say 'innerlich'.
Julian bleibt ruhig, obwohl er innerlich sehr nervös ist.
Julian stays calm, although inwardly he is very nervous.
Von innen sieht das alte Haus viel heller aus als von außen.
From the inside, the old house looks much brighter than from the outside.