"Sanitizer solution" could be either.
And Star-San and Sani-Clean are not the same, but they're more similar than they are different. Both are phosphoric acid sanitizers, with different surfactants giving them different foaming properties. It's possible that their lifetimes are radically different, but I haven't seen any reason to think that would be the case.
I stand by my statement. Sanitizer solutions may lose their effectiveness after being stored for some time under some conditions. That doesn't mean it's always going to happen, but you do need to assess whether it's still effective after storage.
In my experience, also, a lot more grows in the ex-sanitizer than would grow in a bucket of water, so something in that bucket is encouraging the bacterial growth. I don't know whether it's the sanitizer itself or sugars and whatever that rinsed off of things that were sanitized in the bucket, though.