I like to think of minds and memories to be different from each other, or at least to a certain degree. It would help explain LW, for instance; whereas LW would inherit Terra's mind, Xehanort would keep hold of his memories. Or, Xion or Roxas with Sora's memories. They would experience the memories, but not necessarily manifest his mind, or consciousness. In theory, anyways.
The LS having Terra's actual mind idea is shot though since we see that conscious mind debating with MX's within the Apprentice during Blank Points.
The LS is said to be Terra's lingering thoughts by Nomura so that to me makes it more of an extension of Terra's mind rather than the actual thing.
Hmm I can't agree with that theory. I won't say their exactly the same but memories are a key component to the mind, the mind is built of them as it were, I don't think their entirely separable.
Within KH the heart and mind seem more or less the same as the heart is that person. Or at the very least the "mind" is the identity a heart forms for itself.
We see this with Sora and Ansem who both became a being with only a heart. The memories appear to be a key component in that makeup as well since by Sora regaining his mind, form and keeping his memories left Roxas blank.
We know nobodies retain their human memory and from what we've seen in the normal cases, that nobody bases a identity for itself based on those memories which seems to make them nearly the same as the human counterpart.
Given enough time and the right conditions the nobody will then form a heart based on the new memories and experiences gained further showing that memories help form the heart and the mind is the identity the heart identifies itself by.
It's all just to big an interconnected web for them to be simply separate concepts. Also, now that I've typed all this, makes me realize that it seems to work in the reverse of your idea when you look at it. o_0
People's hearts and minds grow from experiences, bonds and the memory of those things. The nobody inherits those memories, taking on a similar mind to the human and grows heart-wise from there all over again.