The words overlap, so here is what they mean in practice.
Przychodnia is a health centre: a building with several outpatient clinics under one roof. Poradnia is one clinic within it, usually a specialist one, for example a poradnia ginekologiczna. In everyday speech people use the two words interchangeably, so do not worry if the receptionist says one and the sign says the other.
POZ (podstawowa opieka zdrowotna) is primary care: your GP practice. On the NFZ you register with a GP by signing a declaration. You do not need to go through your GP to see me.
Poradnia specjalistyczna is specialist outpatient care, where NFZ gynaecology happens. My NFZ clinic in Ogrodzieniec is one of these.
Szpital is a hospital, with wards (oddziały). SOR (szpitalny oddział ratunkowy) is A&E, for emergencies. Smaller hospitals without an SOR have an izba przyjęć, an admissions unit, which also takes emergencies.
Prywatny gabinet is a private consulting room, often one doctor. Centrum medyczne is a private medical centre with several specialists, such as the two where I see private patients.
Nocna i świąteczna opieka zdrowotna is the out-of-hours GP service, open from 18:00 to 8:00 on weekdays and around the clock at weekends and on public holidays. There is more on it in the section on emergencies.
Which one do you need? For a routine appointment, contraception, screening, menopause or a pregnancy check: a poradnia ginekologiczna on the NFZ, or a private centre. For something acute but not dangerous, out of hours: the out-of-hours service. For heavy bleeding, severe pain or anything that frightens you: the nearest hospital with a gynaecology and obstetrics ward, or 112.