hager
gaunt
Describes a person who is very thin and bony, often in a way that looks unhealthy or caused by deprivation.
Der alte Mann hatte ein hageres Gesicht mit tief liegenden Augen.
The old man had a gaunt face with deep-set eyes.

gaunt
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gaunt
Describes a person who is very thin and bony, often in a way that looks unhealthy or caused by deprivation.
Der alte Mann hatte ein hageres Gesicht mit tief liegenden Augen.
The old man had a gaunt face with deep-set eyes.

'Hager' (gaunt) does not just mean 'dünn' (thin). It often has a negative or concerned connotation and describes a person who looks bony and skinny, possibly because of illness, age, or hard work.
Nach seiner langen Krankheit war er sehr hager geworden.
After his long illness, he had become very gaunt.
This adjective is used almost exclusively to describe people or their body parts. Typical combinations are 'eine hagere Gestalt' (a gaunt figure), 'ein hagerer Mann' (a gaunt man), or 'ein hageres Gesicht' (a gaunt face).
Eine hagere Gestalt trat aus dem Schatten hervor.
A gaunt figure emerged from the shadows.
'Hager' (gaunt) is often used with the verb 'wirken' (to seem, to appear) to describe an impression. This combination is very natural when describing a person's appearance.
Der Wanderer wirkte hager und erschöpft.
The hiker appeared gaunt and exhausted.
thin
'dünn' and 'hager' can both describe a person with little body fat. 'dünn' is more general and can be neutral, depending on the situation; it can also simply mean the opposite of strong-built or fat. 'hager' is stronger and describes someone who looks very thin and bony, often rather unhealthy or exhausted. The words can be confused because both describe the appearance of a slim person. If you only want to say generally that someone weighs little, 'dünn' fits. If the person looks very skinny and angular, 'hager' is more precise.

Der alte Mann wirkte hager und sehr müde.
The old man looked gaunt and very tired.
Nach der Krankheit ist er deutlich dünner geworden.
After the illness, he became noticeably thinner.