Informally, CCA2 does not permit any kind of modification of ciphertexts, while RCCA permits some alteration as long as it does not alter the original message. For example, imagine anthink of a publicly randomizable encryption scheme, that is, a scheme that permits to alter the original randomness used during encryption. CCA2 CCA2 would consider these ciphertexts as invalid, while RCCA would accept them.
In the indistinguishability game (IND), this difference is translated in the restrictions to the use of the decryption oracle in phase 2. In CCA-2, the adversary is not allowed to ask for the decryption of the challenge ciphertext $c^*$, while in RCCA, if the adversary asks for the decryption of any ciphertext that decrypts to the challenge messages $m_0$ and $m_1$, he will only receive a special symbol $\mathsf{test}$.