I think in terms of the way one feels, “security” and “safety” may mean the same. I’m inclined to say that they are synonymous in this context. That is, if I feel safe, I wouldn’t hesitate to say that I feel secure.
On the other hand, “security” also refers to documents, especially those related to finance and investment. Similarly, “safety” is also commonly used to mean “a safe place.” In both situations, the words are used as nouns, yet their meanings are different and, importantly, not interchangeable.
I am merely trying to suggest that they have similar meanings in some contexts, but not all.