die Hülle
cover / case
An outer layer, packaging, or casing that encloses something in order to protect it or hold it together.
Ich habe mir eine neue Hülle für mein Smartphone gekauft.
I bought myself a new case for my smartphone.

cover / shell
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cover / case
An outer layer, packaging, or casing that encloses something in order to protect it or hold it together.
Ich habe mir eine neue Hülle für mein Smartphone gekauft.
I bought myself a new case for my smartphone.

'Die Hülle' belongs to the verb '(um)hüllen', which means 'to wrap' or 'to surround'. So the 'Hülle' is what encloses something.
Der Nebel hüllte die ganze Stadt ein.
The fog enveloped the whole city.
The word 'Hülle' is very productive and forms many useful compound nouns. Examples include 'Handyhülle' (phone case), 'Schutzhülle' (protective cover), 'Plastikhülle' (plastic sleeve), or 'Kissenhülle' (pillowcase).
Ohne eine Schutzhülle geht mein Handy schnell kaputt.
Without a protective case, my phone breaks quickly.
The expression 'in Hülle und Fülle' is a fixed unit and means 'a great deal' or 'in abundance'. The words cannot be changed or separated.
Auf dem Buffet gab es Essen und Trinken in Hülle und Fülle.
At the buffet, there was food and drink in abundance.
The meaning 'Körper als Hülle der Seele' (body as the shell of the soul) is philosophical or literary. This meaning is not used in normal everyday life.
Der Roman beschreibt den Körper als vergängliche Hülle.
The novel describes the body as a transient shell.
body
'Körper' and 'Hülle' can both refer to the physical part of a person. 'Körper' is the normal word for the whole physical human body or an animal's body, including organs, muscles, and bones. In this meaning, 'Hülle' refers more to the outward appearance and is often contrasted with the inner self, the mind, or the soul. That is why 'Hülle' sounds much more figurative and not as neutral. Learners may confuse the words because both describe something physical. In everyday language, you almost always say 'Körper'. 'Hülle' only fits when you deliberately separate the outer form from what is inside.

Für ihn war der Körper nur eine Hülle, wichtiger war der Charakter.
For him, the body was only a shell; character was more important.
Nach dem langen Lauf braucht mein Körper eine Pause.
After the long run, my body needs a break.