"She went to the clothing store to go shopping."
Translation:그녀는 쇼핑하러 옷가게에 갔어요.
This sentence would look quite differently in North Korean standard: 《그는 장보러 옷상점에 갔어요.》. This is because: word 《그녀》 does not exist in NK and 그 is used universally for men and women. Word 쇼핑 can't be found in Northern dictionaries, 물건 사다 or 장보다 would be replacements (AFAIK these two can be also used in South Korea, so if you are anti-konglish - here you go). Finally, while 《가게》 would've been easily understood, 상점 is much, much more common word for a shop there.
장을 보다 > 장보다. go shopping. (especially in traditional market or for necessities.) '장' means '시장' (market) here.
'장부다' is an informal abridged form of '장부이다.'
장부 can mean 1) account book or 2) a short form of '대장부'(a brave and manly man). Other words can be made from many homophonic? /homophonical?/homophonal? sino-korean morphemes, but those two are what average native Koreans can think of immediately.
▪그녀는 쇼핑하러 옷가게에 갔어요. She went to the clothing store to shop.
=> "(으)러" (= 기 위해, in order to/so as to; so that) is a subordinate conjunction.
It is used to indicate the sub action (described by the attached clause) is the purpose of the main action (described by the main clause).
쇼핑하다 (= to shop) is the purpose of 옷가게에 가다 (= to go to the clothing store)
▪그녀는 옷가게에 가서 쇼핑했어요. She went to the clothes store, so then she shopped.
=> "어/아서" (= so then; and consequently/and as a result) is a coordinating conjunction.
It is used to join two clauses making them one sentence, by introducing the consequence concept. There is no main clause or sub clause with the use of 어/아서.
It indicates simply that the attached clause has as result, the succeeding clause.
옷가게에 가다 (= to go to the clothing store) results in 쇼핑하다 (= to shop) to take place.
This sentence seems to imply 쇼핑하다 is more incidental than intentional as expressed in DLG's sentence.