Is there a way for a third party to determine whether 2 addresses have been created from the same private key or not?

Question

My goal is to create multiple addresses that are trully unreleated to each other. I'm aware that there's a way to do it in such a way that they'll be derived from the same private key. But will they then be trully unreleated to each other?

For a third party observer, is there a way to determine whether 2 addresses have been created, derived or generated from the same private key, or seed phrase, or from different ones?

update, repharsed

when (a) the same public key is used to generate a first group of addresses

vs

(b) multiple public keys are used to generate a second group of addresses

.... and when the addresses in these 2 groups get shuffled...

(1) is there a way for a third party to deduce the amount of public keys used to generate all of these addresses?

(2) or at least guess whether it was a single public key, or multiple ones?

Answer 1

First. No you will not be able to tell if addresses are from the same key.

Trully unrelated, in your context, I would say that they are related if they are derived from the same seed. If I understand correctly.

Addresses are generated from a public key that is generated from a Hierarchical Deterministic key pair.

From one seed you can generate multiple account, addresses, for any currency.

The seed is created with BIP39. From that seed you can derive path and create other key pair.

Any keys derived from that seed would be related to that root seed.

If you generate another seed, then your accounts could be considered unrelated.