Lisa H. answered 10/16/19
Experienced Korean Language Teaching in the Private School
As you said, it is very similar meaning and I agree with your opinion but it can be used differently in many different situations.
종류- kind of something ( group of objects/places/varieties)
ex) I like kind of spicy foods. = 나는 매운음식 종류를 좋아합니다.
I don't like kind of noisy places. = 나는 시끄러운종류의 장소를 좋아하지 않습니다.
Is tomato one of fruit varieties? = 토마토는 과일종류 중에 하나입니까?
유형- type ( group of categories - using more abstract concept )
ex) I don't like authoritative type of person( authoritative person type ) = 나는 권위적유형의 사람을 좋아하지 않습니다. / 나는 권위적사람의 유형을 좋아하지 않습니다.
I hope this examples are helpful for you.