"Two types one is [type 1] and one is [type 2]" vs "Two types one is [type 1] and other is [type 2]"

Question

Which one of the following is grammatically correct?

Two types, one is [type 1] and one is [type 2]

OR

Two types, one is [type 1] and other is [type 2]

To me the second one sounds correct but I am not sure about the first one.

Example :

1. There are two types of relationships. One is needs based and other is love based.
2. There are two types of caches. One is Write-through cache and one is Write-back cache.

Answer 1

You must use the with other:

There are two types of relationship. One is needs-based and the other is love-based.

This is perfectly fine:

There are two types of relationship. One is needs-based and one is love-based.

You don't actually need either structure. There is an old joke which goes:

There are 10 kinds of people in the word: those who understand binary and those who don't.

(I chose to hypenate "needs-based" but this is a personal style choice.)