The most I've been able to come up with is that fetuses are embryos slightly farther along in their development. Is that correct?
Yes, you are correct. You can read the wikipedia article about an embryo:
An embryo is a multicellular diploid eukaryote in its earliest stage of development, from the >time of first cell division until birth, hatching, or germination. In humans, it is called an >embryo until about eight weeks after fertilization (i.e. ten weeks after the last menstrual >period or LMP), and from then it is instead called a fetus.