What is the difference between Prime Minister, President and Foreign Minister visiting different countries?

In the case of India -

1. The Prime Minister is the daddy (Head of Govt). She/He runs the government as the CEO and is authorized to take calls of any magnitude. No one can question him/her except the Parliament (later, when in session, in case a particular call taken was too stark or unconventional). So, any country that wants actual action will invite the PM over, and then the topmost decision-maker will make himself available.
2. The President is the Head of State, ceremonially. She/He cannot take any major strategic call unless explicitly authorized by the Cabinet headed by the PM. So, it's more of a courtesy or filling in the gap when the PM can't go or is someplace else. So, when a ceremonial presence is required but no real decision-making, the President may be invited.
3. The Foreign Minister works under the PM's direct control and exercises her/his discretion and competency to offer solutions. But final call is the PM's. So, in the basic rounds of groundwork-laying, the FoM can visit.

In all cases, remember that there is a huge administrative machinery working behind the scenes doing the grunt work, supplying facts and intelligence and writing the fine print. 

In case of today's China, the President Xi Jinping has practically centralized all power in his hands (Head of State, Head of Military Commission, Chief of Communist Party, Key decision-maker on economy, etc.) and everyone else seems sidelined.

In the USA, it's the President's writ that runs through and through, subject to constitutional checks.

Source:https://www.quora.com/What-is-the-difference-between-Prime-Minister-President-and-Foreign-Minister-visiting-different-countries/answer/Sandeep-Manudhane