Is the estrogen that can cause breast cancer the same estrogen that can cause uterine cancer, and vice versa?

Yes. In both cases, the reason is due to the activities of estrogen receptor (specifically Estrogen Receptor alpha), which is known to be a tumour promoter.

Endometrial cancer is a type of uterine cancer that involves the lining of the uterus. It is seen in women who take estrogen-only and still have a uterus. This is due to estrogen's effect on this lining, which builds up with prolonged estrogen stimulation. When this occurs, endometrial hyperplasia can result. Tamoxifen, an agent that can reduce the risk of developing breast cancer, can also cause endometrial cancer due to its similar effect on the endometrial lining.

Before menopause, the ovaries are the major source of the 2 main types of female hormones: estrogen and progesterone. The balance between these hormones changes during a woman's menstrual cycle each month. This produces a woman's monthly periods and keeps the endometrium healthy. A shift in the balance of these hormones toward more estrogen increases a woman's risk for developing endometrial cancer.