it is explained throughly in the first pages of the first chapter...
His water proficiency is E, but it has a bonus from his subjects (hence the "+ S", not "vs S") and his overall ranking change because of that. Since he was born a noble, he already started with E + S (if he was a mechant son or something, it'd probably be E + B or something like that). When he was recognized as a Prince by the King, it changed to E + SS (considering he has more power and subjects now). After he adquired the Sword (since it has a will it was considered a subject too), it became E + SSS.
it is E + SSS now because the sword upgraded the skill (since it is a powerful subject).
your question doesn't make sense, because for some reason you're considering his innate rank and his bonus rank at the same time.
for other people, it doesn't show his innate rank (which is E). That's why others see SSS now. It was SS before he acquired the sword. Your question should be "what is the difference between a SS vs SSS rank?", and tbh the power levels haven't been shown yet, so it doesn't matter