It's a very complicated question. For example my aunt and grandma both had breast cancer. My Gyn tells me it's too dangerous to take HRT.
Estradiol is one form of estrogen and is (or at least used to be) considered HRT (Hormone Replacement Therapy) although some refer to it as ET (estrogen therapy).
There is estrogen-only HRT and combined (estrogen plus progestin or progesterone) HRT. Women who have a uterus who take HRT must take progestin or progesterone if they take estrogen in order to protect their uterine lining from the proliferative effects of estrogen.
Estrogen is not associated with an increased risk of any type of cancer (except endometrial/uterine). Studies that compared estrogen-only HRT with combine HRT showed an increased risk of breast cancer for combined but NOT for estrogen-only.
Intact women's ovaries produce hormones into their 80's for optimal health and well-being. Women whose ovaries were removed or failed from loss of blood flow after hysterectomy have an increased risk for a number of health problems due to estrogen deficiency (and possibly testosterone deficiency too). These include heart disease, osteoporosis, dementia, Parkinsonism, cognitive and memory impairment, mood disorders (mood swings, depression), anxiety, poor sleep quality, visual changes, skin changes, muscle wasting, hot flushes, vaginal atrophy. Estrogen "replacement" mitigates some of these risks as well as restoring some quality of life.
As far as your question about estradiol versus HRT, you may be referring to "bio-identical" versus synthetic. The estradiol patches, pills, and gels are considered "bio-identical" and can be purchased at retail pharmacies with a prescription. There are also synthetic forms of estrogen that can be just as effective. A couple that come to mind are Premarin and Enjuvia that are made of conjugated estrogens.
Unfortunately, HRT is very much trial and error. What forms and doses work for one woman may be a miserable failure for another. I personally found generic Estrace (micronized estradiol tablets) to work better for me than the patch. And a bonus is that it is a $4 (for 30) / $10 (for 90) prescription whereas I think I was paying $70 for a 3 month supply of patches.