You are seeing the past.

Light takes time t = d/c to cross the distance d; during that time, an object moving at speed v drifts s = vt from where its light shows it. The slider spans a representative near-to-far distance range for each object. Every speed here is a speed relative to Earth, which is what determines how far an object appears to have shifted — motion Earth shares doesn't count. That's why the Sun uses Earth's own 29.8 km/s orbital speed rather than the Sun's 220 km/s orbit around the galactic centre, which Earth is carried along with; for the planets, their orbital speed is a close enough stand-in for the full relative velocity. Distance in the diagram is compressed so both bodies fit on screen, but the drift offset is drawn to the object's own diameter, honestly — when that offset is too small to see (Andromeda's proper motion barely moves it during ~2.5 million years of light-travel time relative to its own vast size), a magnified inset makes it legible.