Admittedly, looks like I was wrong.
Some connection still (both being a mass of snakes - people eating their snakes to get stronger - Androssi having a familiar feeling), but it looks like SS was locked up since his discovery and stayed in the bowl all this time. Previously, he lived a hidden life, just replicating himself every year because why not.
Thus, no room for SS and SC being the same entity.
Also, the 'copulation' scene with Laura (I was at least right about her doing as much with a snake... eh) was the SS. Which is... just gross and disappointing. At least SC can look like a human convincingly. She just did what she had to, while Rei watched. Thanks for that, SIU.
There's still room that SC is one of the SS's spin-off snakes, a being that ate his snakes, or just a similar species that also has some special princess connection. TBD