An egg is not an embryo. It’s an egg cell that can receive sperm to become fertilized. Then it starts to grow and is called an embryo. In species where the embryo develops inside its mother, it is called a fetus in later stages.

Further reading: https://en.wikipedia.org/wiki/Animal_embryonic_development#Fertilization_and_the_zygote

The reason why I added the ‘not in chicken’ disclaimer is because bees, for instance, do develop without fertilization. But I don’t know enough about that to elaborate further.