Blowfish Cipher, a symmetric block cipher, ensures that two identical plaintext blocks do not encrypt to the same ciphertext block by using different keys for each encryption. This is achieved through key-dependent S-boxes and P-arrays which are initialized during the pre-computation phase of Blowfish. The 16-round Feistel network then uses these unique keys in every round of encryption, ensuring distinct ciphertexts even from identical plaintexts.