Zygote
A zygote or a zygocyte is the original cell that comes to creation when a new organism is formed through sexual reproduction.
A zygote is formed from the synthesis resulting out of the union of the two distinctive gametes
Zygote is the first stage in the development process of an organism.
It is produced of the process of fertilization occurring amongst the haploid ovum cell from the female and the haploid sperm cell from the male.
Embryo
the embryo is the mutlicellular diploid eukaryote in one of the early stages of development. The eukaryote is termed as the embryo, in humans, 8 weeks past the fertilization.
Embryo refers to that stage in the developing process of the organism which starts from the initiation of the first cell division till the birth (till hatching in amphibians and aves and germination in case of plants).
The developing process of the embryo is termed as embryogenesis.