Hi . Its is actually an ambiguous terminology. However, you can think like 길 as "way" and 거리 as " street ".

길 means a way(most of its senses), road, pathway, and a means of doing something. 거리 has a much narrower meaning as a street or boulevard where cars and people pass by. So 길 focus on getting to one's destination, while 거리 is just a place, usually in the city, where a lot of people and cars are passing by. Examples: - 서울로 가는 길 => The road to Seoul. (road) - 여기서 부산까진 먼 길이다 => It's a long way from here to Busan (journey) - 그 친구를 찾을 길이 없다 => There's no way to find him (way, method) - 뜻이 있는 곳에 길이 있다 => Where there is a will, there is a way (way, solution) - 구도자의 길 => The way of a truth (tao) seeker. - 눈길 => gaze. Sight line. The stare of the eye. - 손길 => touch, movement of a hand. - 발길 => path, movement of the feet. - 거리는 가로등 불빛으로 환했다 => The street was brightly lit by the street lights. - 토요일 거리엔 행인들이 넘쳤다 => The Saturday street was overflowing with passers-by. Busy streets are also called 길거리, a compound word made of the two words. - 골목 안에서만 놀고 길거리엔 나가지 마 => Play staying in the alleyway. Don't go out to the street.

Hi, I've already asked this question and here's the answer :) https://www.italki.com/question/380555