I have adenomyosis. Is that the same as endometriosis?

No. There is normally hormonally active tissue in the middle of the uterus which causes you to get a menstrual period. When that tissue gets into the muscle of the uterus that is adenomyosis. When it gets outside the uterus (or on the outer surface) that is endometriosis.
Cousins. Both conditions often coexists in the same patient. In endometriosis tissue that resembles endometrium is ectopic or out of the uterus into other pelvic organs like the ovaries and appendix. In adenomyosis the endometrium is within the uterus but buried into the muscular layer of the womb causing symptoms of pain and excess menstruation. See arrows in this mri.