I want to know whether the bitcoin network generates the same signature for each transaction, because people have only one signature?
No, according to the bitcoin network, the system generates a different digital signature for each transaction. Because the sender generates a digital signature from a transaction message and his private key.
A signature is an intermediary that proves you have a password without seeing the private key due to the math algorithm.
Bitcoin uses the Elliptic Curve Digital Signature Algorithm (ECDSA). While people in the physical world use their unique signature to authenticate when accepting documents or contracts, digital signatures are cryptographic commitments by the owner of a private key corresponding to one specific message (which in this case is the Bitcoin transaction).
As the inputs to the signature generation algorithm are the message and the private key, different messages produce different signatures.