What's the difference between
своя и т.д.) and
моя и т.д.) when Russian people speak they seem aware of the difference but still I can't wrap my head around it.
What's the difference between
In this meaning свой means "belonging to the last agent in the sentence".
Алиса отдала Бобу свои деньги // Alice gave Bob her own (Alice's) money
Боб отдал Алисе свои деньги // Bob gave Alice his own (Bob's) money
Алиса отдала Бобу его деньги // Alice gave Bob his (not necessarily Bob's) money
Алиса отдала Бобу её деньги // Alice gave Bob her (not necessarily Alice's) money
The last phrase is normally only used in Russian when "her" means "belonging to a third female person, neither the subject nor object of the sentence", that third person being obvious from the context.
Ева дала Алисе пальто. Алиса отдала её пальто Бобу.
Ева дала Алисе пальто. Алиса отдала своё пальто Бобу.
The "last agent" thing might be a little bit confusing, as sometimes it's not clear what the agent is.
Алиса дала Бобу своё пальто // Alice gave Bob her coat
Bob's definitely not the agent here, so своё unequivocally means "Alice's"
Алиса попросила Боба постирать своё пальто // Alice asked Bob to wash his coat.
Alice and Bob are both agents (Alice asks, Bob washes), but Bob goes last in the sentence.
Алиса попросила у Боба постирать своё пальто // Alice asked Bob for washing her (or his) coat
This is a bit confusing, as it's not clear who'll be doing the washing, so not clear whether Bob is an agent here or not. This sentence can be interpreted both ways.
Note that the "last agent" rule only works within a single sentence clause, it does not work across dependent clauses:
Алиса любит своих детей. // Alice loves her kids
*Алиса хочет, чтобы свои дети любили её // This is ungrammatical
Алиса хочет, чтобы её дети любили её // Alice wants her kids to love her.
You can't use свои in the second sentence, as on this dependency level there is no agent before свои.
Свой is a nice word which allows to enliven the speech avoiding those permanent occurences of pairs me / my (or you / your and so on).
As a rule of thumb, try not to use я/мой, ты/твой etc. both in the same sentence but replace "мой" (or "твой", "его" etc.) with "свой".
You may think that "I am in my room" looks OK, but Russian people hate sentences such as "Я в моей комнате". In Russian it sounds as if you state twice that it's your room, because your companion doubts this.
To say it short, "свой" has no additional meaning except "мой" / "твой" / "его" but you have to use this word often to speak Russian well.
As I understood, the difference is that "свой" means to be owned by object/subject which you are talking about. "Она взяла свой кофе", "Он взял свой телефон"
But in the case of "мой", you should use it when you(teller) own this object, but it is connected to other person/people. "Егор взял мой телефон", "Анна вошла в мой кабинет".
In case if the subject is you (you're telling from 1st person), you should use "свой".