Zygote is formed after fusion of male and female gametes (sperm and ovum) during fertilization. Zygote starts cell division and gradually develops into an Embryo.
Zygote is a single cell where as embryo is multicellular.
Zygote is the first stage of development; embryo is the stage that follows next.
Zygote is formed by the process of fertilization whereas embryo is formed by the process of embryogenesis.