This subject of the definition of Beings in terms of lineages is something (i.e. a metaphysical assumption) that turns-out to be of the greatest importance - as it gradually sinks-in. There is a half-way understanding of this point, which is an incoherent hybrid - but when taken seriously this changes 'everything'.
I first came across this discussion in evolutionary biology, discussing the idea of homology. For example, the arm of a man is homologous with the wing of a bird. This means that both have the same evolutionary lineage - it is assumed that the bird's wing and human arm evolved from the limb of some more ancient animal ('common ancestor', some kind of reptile, presumably).
Here lineage implies continuity - that there is a continuous and unbroken series of parents and offspring, that link the bird wing and the human arm.
In contrast "convergent evolution" can lead to structurally or functionally similar structures but from a different lineage. The bat's wing is not derived from evolution of the reptile limb, but mostly from the mammalian hand. So the bat's wing can be called analogous with the bird's wing, but homologous with the human hand.
(And the extinct pterasaur's wing is mostly mostly with the ring finger of a reptilian ancestor!)
In the wing example, different lineages are reflected in the bone structure - but one can imagine identical structures that have arisen from different lineages. (This never actually happens in anatomy (I don't think) - presumably massively improbable due to the role of 'chance' in natural selection; but it can be imagined.)
However the reverse often happens - that an homologous structure is functionally very different. Example are among the hormone-secreting endocrine glands. The anterior pineal gland is evolutionarily homologous with an ancestral 'nose' (in some aquatic chordate)! Or (better known) the pineal gland is homologous with a reptilian 'third eye'.
So, here we have a definition of commonality distinguished either on the basis of lineage, or similarity of structure or function; but where the two definitions are not necessarily present at the same time in the same place. There is similarity of structure/ function and there is relationship by lineage - and we can infer one, or the other, or both.
This distinction of similarity can also be applied to identity. What gives Joe Bloggs his identity as JB? Is Joe aged 21 identical with Joe aged 2? First of all is he identical in structure/ function?...
Obviously not. 21 year old Joe doesn't look the same, doesn't do the same things as when 2 years old. Yet we say he is still Joe, and has been Joe (without interruption) throughout the intervening years. So we can see that our real-life, spontaneous definition of human identity is more like 'lineage' than being related to structural or functional considerations.
I think we could say that Joe now is the same as Joe then, because his existence was continuous. And Joe would still be Joe even if he changed his structure and behaviour - even if he underwent transformation. Even if that transformation was so complete as utterly to replace the structure and lead to wholly different behaviour. Identity is preserved by continuity of existence or 'lineage'.
(Just as we regard the caterpillar, chrysalis and butterfly as the same individual - through their radically-transforming metamorphoses - because of their continuity of existence.)
Rather than the lineage of parents-offspring, Joe Bloggs remains the same person because he is A Being who has continuously existed as such, each transformation of Joe's structure/ function proceeding continuously from the previous.
By contrast, as a thought-experiment; an imaginary android-replicant that (apparently) looked and behaved identically with Joe Bloggs, would Not be Joe Bloggs - that is would not be Joe according to spontaneous, human, common sense discernment.
Clearly; our natural definition of identity is based on lineage, on continuity of existence - not based on structural and functional considerations*. And, as so often, the natural (the child-like) is true.
What I end-up with; is the idea of dividing-up reality, of defining the bounds-of and distinction-between 'things' in terms of their lineage/ continous existence - rather than cross-sectionally, in terms of attributes, appearances, definitions or descriptions.
I then realised that this was 'a matter of time'. We nearly always leave time out of our distinctions and definitions. We look at phenomena as-if reality was to be found in an infinitily-small cross-section of time! - So small that time can be left-out of the definition.
But the identity of Joe Bloggs includes time, indeed the being of Joe is potentially endless - in both directions, with roots in the past and the potential for continued existence in the future.
One could say that Joe Bloggs is a 'process' - but that is a physics word. Really Joe just is a person, which is a type of Being; and the idea of a Being is one that even small children understand. Spontaneously. Including that thchildren understand that a being always extends back in time, is 'in' time.
Instead of the infinitely thin time-slice world of mainstream theology, philosophy, science etc.; we have instead a world of Beings, each of which is something-like an infinitely long thread traversing-through time. We can look at that thread at different time-points, but the Being is that thread, as it goes-through time: dynamic, in time...
But more accurately, time and the Being cannot be separated; because Being is inseperable-from time. We could say that Be-ing is itself an 'ing' kind of thing; that is alive, happen-ing, and therefore across-time.
So that Being entails time, requires time; time is included-in/ part-of the definition of a Being. When we identity a Being we are therefore identifying an entity that is the merely current instant (here, then gone) of a lineage, going-back through time, transforming.
And I end-up with a very different way of understanding, knowing, experiencing the world: the world in its ultimate essence, at the bottom-line (ie. metaphysics).
Instead of the mainstream notion of a universe of Things, interacting by Laws of Science, and regarding Time as (just-another) 'dimension'; we instead have instead a living-world of (perhaps-transforming) Beings-in-Time... Beings which may have relationships with each other.
*Set aside the question of whether the discerning person may be mistaken. I am talking about what the discerning person knows truly. If we know truly that a replicant was not continuous with Joe, we would not regard it as Joe. And if we know truly that somebody that neither looked nor behaved like Joe was a result of continuous existence (and transformation); then it would still be Joe - just like the adult Joe is still Joe despite any perceptible resemblance to the baby Joe.)