Kinda, a sperm and egg cell are both gametes that contain half of your chromosomal genome. When they are combined they form a zygote (a fertilized egg) the sperm is far smaller, however and has a tail to it can swim to reach the egg. Egg cells can't move so have few mitochondria as they don't need to respire, while sperm cells have many as they are active all of the time. So in terms of genetic makeup, a sperm either has X or Y Chromosomes while an egg is always X. This means when they combine to make the zygote, the zygote will either be XY (a boy) or XX (a girl). In conclusion they are both sex cells (gametes), with the same job but they are adapted differently to suit this job of producing the zygote.