There are a lot of theoreticians who don´t have a clue of the applied aspects involving cryptography. Are the two disciplines mutually exclusive? Can you learn one without the other?
I cannot tell any obvious feature to differentiate them, but I think you can distinguish theoretical cryptography and applied cryptography from the writing style of papers. In the paper about theoretical cryptography, they usually prove some cryptographic primitive(s) imply another one or construct some schemes or protocols that could be reduced to a standard assumption (e.g., identity-based encryption can be reduced to BDH assumption). Nevertheless, in the paper of applied cryptography, there are usually some implementation results which includes, for example, how to set exact security parameters or message length and so on. Furthermore, theoretical cryptography papers are usually published in conferences like CRYPTO, EUROCRYPT, and TCC, and applied cryptography papers are usually published in conferences like USENIX and ACM CCS.