Yep, in an ovariectomy, they take only the ovaries and leave the uterus in place. The ovaries are needed to produce the hormones that put the heat cycle in motion, so...no, she won't bleed anymore. Removing the ovaries also protects against pyometra (dangerous uterine infection). It is a good option unless the uterus has been around the block too much...many heat cycles, litters, etc. They do get a chance to view the uterus when they go in, and if it looks abnormal in any way, it comes out too.
Which leads to the other point...which is that both ovariectomy and ovariohysterectomy can be performed either traditionally/open or laparoscopically/keyhole. Hard to find a vet that is comfortable with taking ovaries only in an open spay in the US, although they apparently do it in Europe all the time.
Hope that helps....