자기 = his/her own thing
while 자신 = himself/herself/yourself
examples :
그는 자기 몸을 좋아해요 = he likes "his own" body
어머니는 자기 딸을 믿어요 = The mother trusts "her own" daughter
저는 제 자신을 믿어요 = I believe in myself
if you use 자신 to mean oneself you can use 자기 before it too
for example ; 그는 자기 자신을 믿어요 = he believes in himself
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I'm learning korean too , I hope you understand what i said !
good luck !!