This is from a native speaker, I was so confused about the difference between the two and a native helped me out by giving me an in depth view! I cut some of it out, but this is it!
Let's say you just talked about a new apple. Then, the indefinite article 'an' is in front of new apple. If you talk about a little bit more about that apple, then it is called 'the' new apple. ์ด/๊ฐ and ์/๋ have similar relationship. ์ด/๊ฐ is used when something is mentioned first and ์/๋ is used to indicate what you have told.
์๋ ์์ ์ ๊ฐ๋ํ ๋๋ฌด๊พผ์ด ํ ๋ช
์ด์์ด์. ๊ทธ ๋๋ฌด๊พผ์ ๊ฐ๋ํ์ง๋ง ์ฐฉํ๊ณ ์น์ ํ์ด์. ์ด๋ ๋ , ๊ทธ๋ ์ฒ ์์ผ๋ก ๋ค์ด๊ฐ๋๋ฐ, ํธ๋์ด๋ฅผ ๋ง๋๊ฒ ๋์์ด์. ํธ๋์ด๋ ๋๋ฌด๊พผ์ ๋ณด์, ์ดํฅ ํ๊ณ ์ธ๋ถ์ง์์ด์.
Once upon a time, there was a woodcutter. The woodcutter was poor but he was good and kind. One day, he went into the forest and met a tiger. When the tiger saw him, it roared at him.
Let's see this fairy-tale like example. When the woodcutter appeared first, the marker ์ด is used, however ๋ is constantly used like after that ๊ทธ ๋๋ฌด๊พผ์ or ๊ทธ๋. It is the same with the tiger. When the tiger saw him, it is translated as ํธ๋์ด๋.
์ด/๊ฐ is used for general statement and ์/๋ is used for contrast.
์ํฌ๊ฐ ์๋ค. ๋ค๋ค ์ค๋นํด!
์ํฌ came. Get ready, everyone!
์ํฌ๋ ์๋๋ฐ, ์ฒ ์๋ ์ ์์ด.
์ํฌ came, but ์ฒ ์ didn't.
The first sentence is for you if you are preparing ๊น์ง ํํฐ(surprise party). In this sentence, you are not interested in other people's coming. ์ํฌ is the main character of this party. There is no contrast, so it is ๊ฐ. In the second sentence, you are comparing ์ฒ ์ and ์ํฌ. That's why ๋s are used in the sentence.
์ฌ๋๋ค์ ๋ง์๋๋ฐ, ์ ๊ฐ ์ฐพ๋ ์ฌ๋์ ์์์ด์.
There were many people, but the person I wanted to find wasn't there.
์ฌ๋๋ค์ด ๋ง์๋๋ฐ, ๊ทธ๋ ๊ฒ ํผ์กํ์ง๋ ์์์ด์.
There were many people, but it was not that crowded.
In the first sentence, the writer wanted to contrast the people (at the place) and the person he was looking for (let's call him ์ฒ ์), so it was ์. This implies that because there were so many people, the writer expected ์ฒ ์ to be there, but he wasn't. In the second one, he just wanted to say it was not that crowded. That's why ์ด is used there. It implies that you don't care about the number of the people, they were just there.
However, if you just want to simply state that there were many people there without emphasizing the contrast between the large number of people and the person you are trying to find, then you can just use ์ด instead of ๋. It is grammatically correct both ways, but the meaning is slightly different.
It is true with the second sentence, too. If you want to emphasize the contrast with common idea(if there are many people, it is crowded), then you can also use ์ there. It implies that although you might think that the place must be crowded because of many people, but it was not.
Like this example, ์/๋ and ์ด/๊ฐ is sometimes interchangeable but it changes the meaning slightly.
3. ์ด/๊ฐ -> Focus on Subject,
์/๋ -> Focus on Description
As you all know, ์ด/๊ฐ is subject marker(์ฃผ๊ฒฉ ์กฐ์ฌ) and ์/๋ is topic marker(์ฃผ์ ๊ฒฉ์กฐ์ฌ, topic is ์ฃผ์ in Korean). As you can guess from the name, ์ฃผ๊ฒฉ์กฐ์ฌ ์/๋ focuses on the subject and topic marker focuses on the topic, in other words, action or description of the subject.
Let's see the difference with these conversations.
A: ๋๊ฐ ์ฌ๋ถ๋ฆํ๋ฌ ๊ฐ์ด์?
A: Who went for the errand?
A: ์ฒ ์๋ ์ง๊ธ ๋ญํด์?
B: ์ฒ ์๋ ์ง๊ธ ์ฌ๋ถ๋ฆํ๋ฌ ๊ฐ์ด์.
A: What is ์ฒ ์ doing now?
B: ์ฒ ์ went for errand.
In the first conversation, A was curious about the person who went for the errand. So, the focus of the answer is the subject. That's why ๊ฐ is used twice like ๋๊ฐ or ์ฒ ์๊ฐ.
In the second conversation, A was curious about what ์ฒ ์ is doing now. So, the focus of the answer is the action. That's why topic marker ๋ is used like ์ฒ ์๋.
In Korean, something trivial or redundant is just deleted, so it becomes clear what is the focus of the question if the answers by B are shortened.
A: ๋๊ฐ ์ฌ๋ถ๋ฆํ๋ฌ ๊ฐ์ด์?
A: ์ฒ ์๋ ์ง๊ธ ๋ญํด์?
4. With other markers or at the end of a verb conjugation
์/๋: to show emphasis
Do you know the auxiliary verbs in English? It is about the verbs like can, will, should, might. They are used to add meaning to the main verb. There are auxiliary markers(๋ณด์กฐ์ฌ) in Korean and ์/๋ are one of them.
As they are auxiliary markers, you can use them with other markers or at the end of a verb conjugation, too. If you listened to this podcast or read the script carefully, you could find one.
์ฌ๋๋ค์ด ๋ง์๋๋ฐ, ๊ทธ๋ ๊ฒ ํผ์กํ์ง๋ ์์์ด์.
In ํผ์กํ์ง๋, ๋ is used to emphasize the meaning, it was not crowded. Therefore, you can just get rid of it, but the meaning, crowded becomes weaker.
์ด์ ์ง์๋ ์ ๋ค์ด๊ฐ์ด?
Did you come back home safely?
์ฌ๊ธฐ๋ถํฐ๋ ๋ด๊ฐ ํ ๊ฒ.
In examples above, ์ง and ์ฌ๊ธฐ are emphasized.
์ด/๊ฐ: to show subject.
Sometimes, ์ด/๊ฐ is used with other markers. It is just used to show the subject of the sentence.
์ฌ๊ธฐ๊น์ง๊ฐ ๋ด๊ฐ ํด ์ค ์ ์๋ ์ ๋ถ๋ค.
This is the everything I can do for you.
์ง๊ธ๋ถํฐ๊ฐ ์ง์ง ์์์ด๋ค.
From now is the real beginning.
5. When the sentences are combined, ์ด/๊ฐ must be used in the sentence in the middle.
If you make the long sentence by combining several sentences, then the sentence used in the middle(it is called ์๊ธด ๋ฌธ์ฅ in Korean) should only use ์ด/๊ฐ.
It is really hard for you to understand what I am saying now, so let's learn with example.
์ํฌ๋ ์ฒ ์์ ๋ง์ ์กฐ์ฉํ ๋ฃ๊ณ ์์๋ค. ์ฒ ์๋ ์ํฌ๊ฐ ์ง์ ๋นจ๋ฆฌ ๋ค์ด๊ฐ๊ธฐ๋ฅผ ๋ฐ๋ผ๋ ๊ฒ ๊ฐ์๋ค.
์ํฌ was listening to what ์ฒ ์ was saying quietly. It seems that ์ฒ ์ wanted ์ํฌ to go back home early.
If we follow the first rule, we should change ์ํฌ๊ฐ in the second sentence to be ์ํฌ๋. Because that's the second time ์ํฌ is mentioned. But the second sentence is combined sentence. It is a combination of ์ฒ ์๋ --๋ฅผ ๋ฐ๋ผ๋ ๊ฒ ๊ฐ์๋ค and ์ํฌ๊ฐ ์ง์ ๋นจ๋ฆฌ ๋ค์ด๊ฐ๋ค. As ์ํฌ๊ฐ ์ง์ ๋นจ๋ฆฌ ๋ค์ด๊ฐ๋ค is in the middle of ์ฒ ์๋ --๋ฅผ ๋ฐ๋ผ๋ ๊ฒ ๊ฐ๋ค, ์ํฌ๊ฐ is used.
Note: I did get permission to share these with you.