That is correct. When an egg is fertilized by a sperm, the fertilized egg is now a single cell with a full complement of chromosomes, called a zygote. The zygote will undergo normal cell division for about a week, at which point it will be called an embryo. The cell division will continue, major organ systems will start to be produced, and in about 8 weeks time, it is now called a fetus. The unborn child will continue to get larger and develop all the rest of its organ systems, until about 40 weeks, full term, it is born into the outside world.
I think you will find this link helpful, as this gets complex.
Basically, when the sperm meets the egg it forms a zygote, a fertilized egg. That egg develops into an embryo, into a fetus, and then the baby is born.