구두 means shoes. 신발 also means shoes. I am not certain of this, but my impression is that I hear the word 신발 in conversation more, while I see the word 구두 on signs more. Perhaps, a certain kind of shoe is more likely to be called 구두, while another 신발. If I find out, I’ll update this. It seems that all kinds of bargain footwear is available in Korea, with shoe sales everywhere you look. As to the quality of these shoes, I am not sure. Certainly, internationally famous brand name shoes are not any cheaper in Korea, and might even be more expensive. But I wouldn’t be surprised if you could get a really nice pair of handmade shoes in Korea. There are certainly a lot of shoe repair shops. These repair shops are often quite cute little box shops on the sidewalks. Here’s a small selection of 구두 and 신발 signs and photos.
This final one was taken in an Apgujeong side street.