Yes, spermatogenesis makes sperm in the testes and oogenesis makes eggs in the ovaries, but there are some other differences.
After the 2 meiotic divisions in a single spermatogonium, you get 4 spermatids, which undergo maturation to form 4 sperm cells, or spermatozoa. They are hardly more than a packet of DNA, with a flagellum powered by mitochondria and an acrosome containing enzymes to penetrate the egg cell membrane.
After the 2 meiotic divisions in the single oogonium, you get one ovum and three polar bodies. Each time the oocyte divides, most of the cytoplasm goes into one product and the other one (the polar body) just gets a set of chromosomes. So the resulting single ovum is quite large compared to a sperm cell.
Another thing. Spermatogenesis goes on in a male from puberty almost until death. In females, oogenesis goes on from before birth until menopause. Females are born with about 40,000 primary oocytes, so they have already begun maturation. The first meiotic division, producing secondary oocytes, occurs after puberty, but the second meiotic division doesn't occur unless fertilization occurs. Secondary oocytes are what gets ovulated, and only one per month.