The signs and so on change, but the Chart is usually the same in terms of Elemental distributions.
For example: someone with many planets in the 3rd House (air house) with Mars as their Chart Ruler, suddenly has Mars in Gemini as their Chart Ruler elsewhere. Someone with a Pisces stellium suddenly has Jupiter in Pisces on an Angle.
What changes depends on what one's fate is, what one chose to invest in or 'inscribe' in the past lifetime and how one was reincarnated, what one's destiny is in that lifetime.
The Quora person isn't completely 'wrong' but it's a lot more complicated than that. Sun and Moon swapping can be rare and tends to be more protracted than this.
What does not change? The degrees are ridiculously similar. The aspects are often eerily similar, creepily so, even if the quality (i.e. square or trine or whatever) changes.
The Moon often represents very important clues to who someone is throughout their lifetimes. It isn't the same sign-wise, but if you add it all together, the symbolism is revealing.
Usually the Ascendant is the same, but occasionally it isn't. Regardless, the Chart Ruler planet is USUALLY the same.
It isn't 'exactly the same', I don't know who started this idea but it is wrong. Hyper-advanced souls can of course choose to incarnate with a near-similar chart, but Pluto orbits for 248 years!