Yes. A hypertensive emergency is when the blood pressure is so high it's caused an acute event. One such example might be a stroke a heart attack or heart failure would be another. A hypertensive urgency is a very high blood pressure but no end organ damage has yet to occur. Either way an aggressive program needs to be implemented to lower the pressure.
Yes. The word emergency means "a condition of urgent need for action or assistance" (american heritage dictionary). If the blood pressure is not seriously elevated, we just call it "high blood pressure". Calling it an emergency, implies that the blood pressure is very seriously elevated and causing distress (like chest pain (angina) or shortness of breath (congestive heart failure).