The transactions from
13u3BwugeQzzD755L7jDV2P81h5vwWveYeTHQMB3BVokkWco have the same hash because they are immortals.
The ones from
16ZbFjyAw1s2xv1bBYBHHGTmbXfokoCE3KYENWL1DDiQAo78 have different hashes because they are mortal.
Assuming that you are using a deterministic signature scheme and since the immortal txs reference the genesis hash, they are the same payload.
Mortal transactions must reference the block hash of their first valid block, so those are of course different.
Our recommendation is to use mortal transactions and one of the reasons is mentioned in our wiki quoted below :
NOTE: If an account is reaped and a user re-funds the
account, then they could replay an immortal transaction. Always
default to using a mortal extrinsic.
Thank you to the external team that asked the question and presented the examples, to Joe Petrowski for giving a super detailed explanation with screenshots & Iker for reviewing.