One mechanism, two geometries. The difference between them is not what happens to the mind; it is what happens to the meat, and when.
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Suppose the year is 20XX, and the latest Personal Digitizer Device has just been released.
Your friends have already made the transition. They were early adopters, as usual. They keep telling you the same thing late adopters have always been told by early adopters: come on in, the water's fine.
You are not so sure.
The device is supposed to let you upload your consciousness at your own pace. It is advertised as user-friendly, gradual, reversible, and specifically designed for Luddites like you: curious enough to wonder, cautious enough not to blindly leap.
The instructions are simple. Keep the device with you. When you are ready, press a button. The device will replace one biological neuron with a synthetic one that performs the same role inside your brain. Unlike earlier models, this version even has an undo feature. The biological neuron is suppressed rather than destroyed, so you can switch it back on if you decide to.
You hesitate.
Then curiosity wins.
You press the button.
Nothing happens.
At least, nothing you can notice. The room is still the room. Your hand is still your hand. The little anxiety in your chest is still yours. You remember deciding. You remember pressing. You are still here.
So you press undo.
Still nothing.
You press the button again.
Still nothing.
You keep pressing. One neuron at a time, then another, then another. Eventually the ritual becomes boring, which is probably the most important fact about it. Terror cannot keep its shape when no step can be made to carry the terror.
At some point you set the device to automatic. It runs in the background, replacing neurons at a casual, steady rate. Biological support decreases. Synthetic support increases. Your friends keep making jokes at your expense. You keep forgetting to be afraid.