The Sun never moves in this picture — it lies out beyond the lit limb, and the Earth turns inside a shadow that stays put. Sunlight fades through the three twilights — civil to −6°, nautical to −12°, astronomical to −18° — so the terminator is a band, not a line.
Behind the Earth the umbra
tapers to a point — away, because the Sun is a disc and not
a spark. Around it the penumbra
widens. At the height of the ISS the umbra is still within half a percent of
the Earth's own radius, which is why a low satellite spends up to
two fifths of every orbit in the dark.
You can see a satellite only where all three things hold at once: it is above your horizon (inside the footprint ring), the Sun still reaches it (gold track), and your own sky has gone dark. That triple overlap is the green patch on the ground — it is where someone is watching the ISS go over right now.