Perhaps not indistinguishable. My point is that nothing meaningful can really be known about either, if it is unknowable.
Put another way: Is there a God? I don’t know. Is there an angry unicorn on the dark side of the moon? I don’t know that either. This illustrates both that neither “fact” can be tested, and also that neither fact has much impact on anything else - both are irrelevant possibilities.
If something can’t be tested, that means it does not interact in any consistent, meaningful way with the rest of reality.
The universal constant is something that is hinted at by experimental observations. No observations point toward God’s existence other than wishy-washy ones like “nature is beautiful/complex”. MAYBE it points toward an intelligent creator, though I don’t think so, but it certainly does not support elaborate ideas like the Trinity, Heaven, Hell, angels, souls etc.