slim
Describes clothing that is cut very close to the body and tight-fitting. The term is often used as 'Slim Fit'.
Ich trage am liebsten Hosen im Slim-Schnitt.
I prefer to wear pants in a slim cut.

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Describes clothing that is cut very close to the body and tight-fitting. The term is often used as 'Slim Fit'.
Ich trage am liebsten Hosen im Slim-Schnitt.
I prefer to wear pants in a slim cut.

As an English loanword, 'slim' is often not declined when it comes before a noun. So you say 'eine slim Jeans' (a slim pair of jeans) and not 'eine slime Jeans'.
Er sucht eine slim geschnittene Jacke.
He is looking for a slim-cut jacket.
You can easily recognize the meaning from the context. If people are talking about clothing ('Hose' (pants), 'Jeans' (jeans), 'Schnitt' (cut)), it refers to the close-fitting cut. If people are talking about products ('Version' (version), 'Konsole' (console), 'Getränk' (drink)), it refers to a reduced variant.
Diese Hose ist mir im Bein zu slim.
These pants are too slim for me in the leg.
The word 'slim' comes from English and is used in German mainly in the fashion industry and in product marketing.
Die Werbung verspricht ein neues, slimeres Design für das Smartphone.
The advertisement promises a new, slimmer design for the smartphone.
You will find 'slim' especially often in the fixed combination 'Slim Fit'. This term describes a very figure-hugging and tight clothing cut.
Ich kaufe meine Hemden immer in Slim Fit, weil sie besser sitzen.
I always buy my shirts in slim fit because they fit better.
far / wide
'weit' and 'slim' can express opposites when talking about clothing. 'weit' then means that a piece of clothing fits loosely or has a lot of room. 'slim' describes clothing that is cut close to the body and tight-fitting, often as 'Slim Fit'. So the difference is not length, but fit. For comfortable, loose clothing, 'weit' fits. For a narrow, tight cut, 'slim' fits.

Für das Bewerbungsgespräch kauft sich Paul ein slim geschnittenes Hemd.
For the job interview, Paul buys himself a slim-cut shirt.
Der Pullover ist mir zu weit, deshalb rutscht er immer von der Schulter.
The sweater is too loose on me, so it keeps slipping off my shoulder.