> except for pre-shared one time pads when used correctly
The relevant property here is known as "information-theoretic security", and I'm not sure if one-time pads are the only way to achieve it, e.g. Shamir's secret sharing also has this property (although the use case is slightly different): https://en.wikipedia.org/wiki/Information-theoretic_security
Isn’t one time pad just a simple version of secret sharing?
you can sort-of view it that way, but it's not particularly useful. There are settings where you can view (steps of) a cryptographic algorithm as applying a one-time pad with a pseudorandom pad (say counter-mode encryption for the most obvious example, though it appears elsewhere as well).
Alternatively, shamir's secret sharing can be extended to threshold settings pretty easily. So you can write a generalized scheme where you only recover things when "enough people" (but perhaps not everyone) tries to reconstruct. This generalized scheme doesn't look particularly like the one-time pad.
So they end up coinciding in the 2-party case over F2 but it seems to be mostly a coincidence.
I would say that SSS is a generalization of OTP, but OTP in practice is so dramatically and unbelievably simpler than SSS that it's not practically useful to consider it as "just" a special-case of SSS. Which is to say, if you were implementing OTP, you would not just implement SSS and then set the right parameters; you would use an entirely distinct implementation.
Those are the only two known algorithms that have this property.