Oop, showing up to infodump again '^^
I'm not sure where the idea that identifying with means "wishing or wanting to be" came from, but it's not really... true? If you long to be [that thing], feel like you should've been [that thing] - that is first and foremost a sign that you are that thing already, on some level, or that you would be happier identifying as it!
If you want to be a nonhuman species, and wish you were it: that isn't a conventional otherheart experience, but it is a pretty understandable experience for an otherkin who doesn't yet know (or accept) that they are nonhuman.
So that's... really not what the difference is between otherhearted and otherkin at all asjkdhaskjhd
It's a widespread misconception nowadays that hurts both otherkin and otherhearted. Otherkin because it can create a loop of self-invalidation ("am I really otherkin, though, or do I just want to be?" This is a nonsense concept! If you want to be then you can be!); otherhearted because it is a fundamental misunderstanding of the experience which reduces it to "otherkin lite" or "not quite kin enough".
I think the focus on the ideas of "identify as" versus "identify with" is part of the problem here, cause those are abstract and ambiguous concepts. There's no guidance given by them - most people couldn't tell you clearly what one means versus the other.
I'll give you my explanation, to the best of my ability.
Otherkin, who identify as nonhuman, perceive themselves on some level as being nonhuman in their own mind, emotions, instincts, cognition, self-perception, or self-image. Not all of these are required to be otherkin, of course - and for some folks there are physical aspects as well, but usually there's going to be a mental or emotional part of the identity too.
Non-physical identity, or identity different from that which you were raised with, can be a hard concept to grasp and certainly a hard one to recognise in yourself. Some people (like yours truly!) have a relatively straightforward time of it - able to simply untether ourselves from the ideas we were raised with, and recognise that the face we see in the mirror isn't necessarily who we are.
Aka, my systemmate, didn't have it so easy. Aka has always wanted to be a dragon. When ae was a kid, it occupied aes mind on a daily basis. Ae had phantom shifts, and played pretend all the time... scrambling around on all fours and roaring and holding aes jacket out on windy days pretending it was wings. But when ae reflected on it, ae just saw longing - not being.
And yet, when I recognised this enough to encourage aem to look deeper - and then ae discussed with some other people as well - ae found that being a dragon feels right. That it brings aem incredible joy. That when we drew up an idea of what ae's dragon might look like, it was euphoric for aem.
And in the end - excitedly - Aka realised that ae is dragonkin.
The longing was a manifestation of an identity that already existed, that Aka just hadn't been able to embrace without a bit of perspective (and encouragement) from friends.
If you see someone say they long to be nonhuman, you're doing them a disservice by pointing them to the otherheart term (which doesn't actually mean that) when otherkin is where they belong.
Now, onto what otherhearted means...
This is a term that means a great deal to me. I am arthropod-hearted. I always have been, I think. It's part of who I am.
I am not an arthropod. I don't want to be an arthropod, and I don't need to be. If anything, I find particular meaning in the connection I have with them despite not being one - that's a genuinely important part of the experience for me. They're so different from me, and yet I care so much for them!
For me, this experience is one of a profoundly deep affection which eclipses what is "normal" for a person to have towards nonhumans. Arthropods are my joy. They are my friends, my charges, and my home. They genuinely feel like one of the brightest lights in my life.
There've been times where I've been deeply depressed and miserable, and been pulled up out of it just by a small encounter with a spider or insect.
It's hard to really articulate exactly what they mean to me. Every arthropod I come across pings in my mind the same way my beloved cat does; I love them, I care about them, I want to protect them and understand them.
This is just... such a purely joyful, positive experience for me. Arthropods are the shape of what life means, for me. They are stars in my sky.
That's not the only way otherheartedness can be experienced. For example, Aka is crustacean-hearted, and aes experience of this is very different from my own!
Aka isn't all thoughtful and introspective in the way I am, and if you ask aem why ae's crustacean-hearted, you'll get a shrug. And if you ask aem what it means to aem, mostly what you'll get is excited incoherence as ae pulls up image after image of squat lobsters and rock crabs and shrimp, flailing and gesturing and saying "they're just little guys!" and "they're so shaped!"
And yet, the joy at the heart of it, I can tell you is the same energy as mine towards all arthropods. It's a kind of... boundless affection, enthusiasm, happiness at the simple fact that these creatures exist and we share the world with them!
It's a very beautiful experience. It's also a very unique and distinct experience. Some otherkin might feel a similar enthusiasm towards their kintype/s, but that comes from a perspective of "these are me" or "these are like me". Otherhearted feelings, on the other hand, are if anything defined by the fact that they aren't you - and yet you love them anyway.
And why would you need to be one, when you can exist alongside them? When you can see them from the outside, appreciate them more deeply from the vantage point of a mind that can learn, understand, and ultimately, even use that knowledge to safeguard them or to help other people see some element of the value in them that you do?
It really does break my heart to see how often, and how widely, otherheartedness is misunderstood. And especially to see it characterised as some impossible longing ("I wish I was this, and yet I'm not") - rather than something positive and joyful, which is embraced through enthusiasm and love for something other.
I'm planning to write up a proper essay on the term at some point... once I've gathered the info I need...
But I hope this can serve as some kind of resource in the meantime. I think correcting this misconception will be better for both otherkin and otherhearts. ^u^