There is no difference; they both refer to the use of prescription medications to increase levels of sex hormones in the body. “Menopausal hormone therapy (MHT)” is the newer term; it has replaced “hormone replacement therapy (HRT)” in many professional and scientific circles over recent years. Either one is acceptable and they mean the same thing.
Visit www.iapmd.org/surgery for lots of evidence-based information and resources for those considering, going through or recovering from surgery for PMDD/PME.