A BIP32 fingerprint consists of the first 4 bytes of HASH160 of the compressed public key: SHA-256 followed by RIPEMD-160. It is 32 bits, usually written as 8 hexadecimal characters. The chain code is not included.
The calculation uses the serialized public key, not seed words or the private key as a direct input. The short fingerprint is an auxiliary identifier; it is not a receiving address, cannot sign a transaction and does not contain the data needed to recover the wallet. [BIP32 — Key identifiers and serialization]
An xpub or xprv record contains the fingerprint of that key’s parent. For a master key, this field is 00000000 because it has no parent; it is not the master key’s own fingerprint. An application may display the master key’s own fingerprint, so check the field’s meaning and derivation level when comparing. [BIP32 — Key identifiers and serialization]
For the master key in BIP32 public test vector 1, its own fingerprint is 3442193e. The parent field in its master xpub remains 00000000. This is a public test example, not a safe foundation for a wallet holding your funds. [BIP32 — Key identifiers and serialization]
Under BIP174, a PSBT associates the master fingerprint with the derivation path for the relevant public key. An Output Descriptor can also specify the origin fingerprint and path. Recognizing change requires more than a matching fingerprint: the signer must derive and compare the actual key and corresponding script conditions. [BIP174 — Key origins and change detection] [BIP380 — Output Script Descriptors]
With 32 bits there are only 4294967296 possible values, so different keys can have the same fingerprint. BIP32 requires software to handle collisions. A match does not verify the complete set of accounts, derivation paths, script types or availability of private keys. [BIP32 — Key identifiers and serialization] [BIP380 — Output Script Descriptors]
Compare the same kind of fingerprint at the same derivation level. A difference may indicate a different seed or passphrase, but first rule out confusion between master and parent fields. Supplement a match by checking known addresses and the correct paths and scripts; the fingerprint alone cannot replace a securely stored backup or a verified recovery procedure. [BIP32 — Key identifiers and serialization] [BIP380 — Output Script Descriptors]
For the clearest picture, read this entry together with HD Wallet, PSBT, BIP39 passphrase, Output Descriptor.