Confusion of “首相” and "总理"
In the constitutional monarchy, 首相 is the the head of the cabinet, with the highest executive power. 

首, in ancient Chinese, means the first or top. 相, short for 丞相, are the officials(usually with great power, just below the emperor) of the emperor. Therefore, 首相 is the top official of a central government.

In the republican state, there is no prime minister, and 总理 run the central government.

Countries have 首相: Japan, UK, Netherlands, Denmark, Belgium...

Countries have 总理: China, Germany, India...
Most countries have a 总理, while USA has neither a 总理 nor a 首相, it has a 国务卿(Secretary of State). 
States with 总理 usually have a 总统(president) or a 主席(chairman).