erworben
acquired
Obtained through learning, work, or purchase, as opposed to innate or inherited.
Sprachkenntnisse sind eine erworbene Fähigkeit, keine angeborene.
Language skills are an acquired ability, not an innate one.

acquired
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acquired
Obtained through learning, work, or purchase, as opposed to innate or inherited.
Sprachkenntnisse sind eine erworbene Fähigkeit, keine angeborene.
Language skills are an acquired ability, not an innate one.

'Erworben' (acquired) is the past participle of the verb 'erwerben' (to acquire), which means 'to get through work, purchase, or learning.' As an adjective, it describes a quality that came about in this way.
Er hat sich im Laufe der Jahre ein großes Wissen erworben.
Over the years, he has acquired a great deal of knowledge.
In its general meaning, 'erworben' (acquired) is often combined with abstract things such as 'Fähigkeiten' (skills), 'Kenntnisse' (knowledge), 'Qualifikationen' (qualifications), or 'ein Ruf' (a reputation).
Seine guten Manieren sind nicht angeboren, sondern mühsam erworben.
His good manners are not innate, but painstakingly acquired.
You can recognize the medical meaning from the context. When terms such as 'Krankheit' (disease), 'Syndrom' (syndrome), 'Immunschwäche' (immune deficiency), or similar words are used, 'erworben' (acquired) means that it is not congenital.
Das erworbene Immundefektsyndrom wird durch ein Virus verursacht.
Acquired immunodeficiency syndrome is caused by a virus.
bought
'gekauft' and 'erworben' can both mean that someone has obtained something. 'gekauft' is more precise when money was paid. It fits well with everyday things, for example clothing, food, or a car. 'erworben' is more general and more formal. You can acquire something by buying it, but also through learning, work, or experience. That is why you are more likely to say 'gekaufte Schuhe' (bought shoes), but 'erworbene Kenntnisse' (acquired knowledge). The words can be confusing because buying is one way of acquiring something. If you want to clearly say that something was paid for, 'gekauft' is more natural.

Durch den Sprachkurs hat Mehmet viele neue Kenntnisse erworben.
Through the language course, Mehmet acquired a lot of new knowledge.
Im Urlaub trägt sie gern das neu gekaufte Kleid.
On vacation, she likes wearing the dress she recently bought.