People do not call sex without birth control "unsafe sex", unless they use non-standard terminology. In standard usage, "unsafe" refers to lack of protection from STI's; see the definition on Wikipedia, which reflects standard usage of the words in modern parlance:

"Safe sex is sexual activity engaged in by people who have taken precautions to protect themselves against sexually transmitted infections (STIs) such as HIV/AIDS.[1] It is also referred to as safer sex or protected sex, while unsafe or unprotected sex is sexual activity engaged in without precautions. Some sources prefer the term safer sex to more precisely reflect the fact that these practices reduce, but do not completely eliminate, the risk of disease transmission.[2] In recent years, the term "sexually transmitted infections" (STIs) has been preferred over "STDs", as it has a broader range of meaning; a person may be infected, and may potentially infect others, without showing signs of disease.[3]"