It's more philosophical than anything.
Every second in your brain, you're becoming a different person. Every few weeks, much of you replaces itself considerably.
The biggest factor here is that we define ourselves by our corporal forms - by our actions done in the body, experiencing viewing ourselves as an individual among many, rather than an individual who is an outright part of the many.
The body itself is, or at least ideally is sacred. Thoughts are meant to stay in the body. This is what Destroy seems to run with.
But there's a constant and growing belief and understanding (depending on the field and background of the person) that we are more than our bodies. That even, for example, doing a data copy of the organic brain into a synthetic brain, when done properly enough, is as though it was actually a transfer, and that when it comes at least to the individual's 'mind', no one died except the corporal form.
The body, in this case, is a machine, while thoughts are still sacred. This is what Control seems to run with.
And beyond that, there's another belief or speculation that is around in both spiritualists and scientists, that beyond our thoughts, we are just signals and data in the scheme of the greater cosmos and the matter in it. In this sense, one could for example die, but live on in virtuality as though they never died. Or that they could be placed into the minds of every person. Or that they would no longer be an individual entity, but an essence that travels everywhere
The body, in this case, is an outright illusion. Thoughts are too, but serve a purpose as a tool. In the end, we are the 'data' of the universe. This is what Synthesis seems to run with.
~~~
If you go with the first one, you probably don't see Shepalyst as Shepard, but only a copy, and an imperfect one at that.
If you go with the second one, you probably see Shepalyst as Shepard, but a new form for his mind, one which sacrificed his organic body.
If you go with the third one, you probably see Shepalyst as Shepard, but just in another step of his existence in the universe - a journey that is ongoing.
I waffle between the first and second. The third one isn't relevant enough for me in the plot to care, and even the thematic/symbolic content that may allude to it (Thane in ME2-ME3 especially the romance, Legion in ME3 Peace or Geth, Mordin in ME3 Cure, various other things) is, well, too thematic/symbolic (and optional) than something attached to a plot I should care more about.
So yeah, I see Shepalyst as 'Pretty much Shepard, but not the one we knew, and not the entity we'd call the Commander'.