A zygote is the first stage of prenatal development and is just a group of non-differentiated cells. An embryo is much larger and its cells begin to differentiate. The zygote phase is directly followed by the embryo stage.
A zygote is formed when a sperm and an egg combine into a single cell. The resulting cell then enters a phase of rapid division in which it quickly grows larger. The cells remain non-differentiated as long as they stay in this rapidly dividing zygote stage. Between the zygote and embryo stages is the blastocyst stage, which creates two layers of cells.
The central layer of cells becomes the embryo; this is when cells begin to differentiate. The cells begin to specialize and take on specific rules instead of all cells being the same, like they were in the previous stages. The organism remains in the embryo stage until all of the essential organs and features have been created. This does not mean that the organs and features are all fully developed however. While in the embryo phase, these features are still very basic and need to continue developing.
After the embryo has grown all of these necessary features, it becomes a fetus. The fetus continues to develop features, organs and systems until these features are fully functional. Once the fetus is fully developed, it is ready for the outside world.