The words reminiscence and memory can be used in similar contexts, but reminiscence suggests the recalling of usually pleasant incidents, experiences, or feelings from a remote past.

// my grandmother's reminiscences of her Iowa girlhood

The words remembrance and memory are synonyms, but do differ in nuance. Specifically, remembrance applies to the act of remembering or the fact of being remembered.

// any remembrance of his deceased wife was painful

Some common synonyms of memory are recollection, remembrance, and reminiscence. While all these words mean "the capacity for or the act of remembering, or the thing remembered," memory applies both to the power of remembering and to what is remembered.

// gifted with a remarkable memory

// that incident was now just a distant memory