I think of soul mates as those you have several of, maybe even dozens, depending on how meaningful they are, but there is always some path for growth with them, or old past life contracts, or even opportunities to resolve current life karma, where they kind of substitute, because you can work it out with them, but not the actual persons from your past. You may or may not have extensive similarities. But when it is as eerily similar as you describe, that sounds to me like a twin soul, maybe you are using the term soul mate to mean something more like a twin.
Wheras kindred spirits to me means the same values and interests, especially spiritual. They could be someone or a group and you may not even know them beyond acquantiance. It's more like when you go to a group eg, to share reiki, or a support group for depression, something like that. Some intuitives describe 'balance partner' too, a more long-lasting mate that resembles twin souls, but for twins there is a lot more of a psychic connection, and spiritual access and changes you have never had or imagined before.
That's how I see it. I don't subscribe to the adage that if they are your twin you will never question it. It is not a decision to take lightly and we are learning to use our head and our heart in a more cooperative new age way, of course you should question it, imo.
Hope that helps- these discussions go round and round as you will see, but there are so many twins meeting now, got to keep helping each other sort it out!
. so thanks for asking ! : )