buffer overrun:
Some prominent vendors and researchers use the term "buffer overrun," but most people use "buffer overflow." See the alternate term for "buffer overflow" for context.
memory safety:
Generally used for techniques that avoid weaknesses related to memory access, such as those identified by CWE-119 and its descendants. However, the term is not formal, and there is likely disagreement between practitioners as to which weaknesses are implicitly covered by the "memory safety" term.