Key length does not change block size
The suffixes 128, 192 and 256 specify key lengths; each AES input/output block is 128 bits. AES adopts particular Rijndael configurations rather than every block size supported by the wider family.
NIST published FIPS 197 in 2001 and updated its presentation and editorial material in 2023 without technical changes to the specified algorithm. A document update therefore differs from replacing the cipher.
References: [1]
State transformations and round keys
The standard represents a block as a 4×4-byte state and applies byte substitution, row shifts, column mixing and round-key addition. AES-128, AES-192 and AES-256 use 10, 12 and 14 rounds: an initial key addition precedes them, and the final round omits column mixing.
Key expansion derives round keys from the input key rather than requesting independent external randomness each round. Accelerated or hardware implementations may organize computation differently while preserving the specified result for a given input and key.
References: [1]
The primitive is not a complete message-protection scheme
Multi-block protection also needs a mode, initialization material and applicable length or padding rules. Independent ECB transformation preserves equality between repeated plaintext blocks, while other modes have their own confidentiality conditions; saying AES alone leaves these unspecified.
Authentication is not supplied merely by the AES name. AES-based authenticated encryption retains nonce and usage obligations, and implementations can leak through timing or caches. FIPS 197 explicitly distinguishes equivalent algorithm implementation from protection against implementation attacks.