In the context of cryptography, what are the differences between a cipher that uses symmetric keys and a cipher that uses asymmetric keys? The industry standard for the size of the RSA public key is...

In the context of cryptography, what are the differences between a cipher that uses symmetric keys and a cipher that uses asymmetric keys? The industry standard for the size of the RSA public key is much bigger than the size of a symmetric key? Why? Are ciphers based on symmetric keys not s secure as RSA?