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I would say there isn't any meaningful distinction. I mean, heck, Wikipedia itself, in the article you linked to, just redirects "security protocol" to "cryptographic protocol", it considers them to be the same thing. That's pretty much true in the world of computing.

If we just look at the terms themselves, the obvious implication is "a cryptographic protocol is a security protocol, implemented with cryptography, and a security protocol is a protocol that provides security, but doesn't necessarily use cryptography". The US system of classified documentation is a decent example, there's all kinds of written protocols about what kinds of information should be classified at what levels (Confidential, Secret, Top Secret), how to label such documents, store them, dispose of them, transfer them between parties, etc. All of that is focused around physical human interactions, but could definitely be described as "security protocols" I.E. "rules and procedures for doing things in a secure manner".

Within the world of computing, security does pretty much all come down to cryptography, so just about anything you could describe as a "security protocol" probably can also be described as a "cryptographic protocol", on account of being fundamentally built on some form of cryptography.