Types of meetings that foreign dignitaries may have:
State visit: the ultimate, with a state dinner, an honor ceremony with 21-gun salute on the White House lawn for a head of state and a 19-gun for a head of government. Visitor also may stay at the presidential guest quarters, Blair House.
Official visit and working visit: may include lunches, meetings or whatever else the host president wants.
The drop-by: the visitor gets a meeting with someone other than the president and the president "happens to drop by" for a few minutes.
The pull-aside: sort of a drop-by in public — the president is attending a public event and meets briefly with the visitor in an anti-chamber.
Private visit: foreign dignitary is in the United States primarily for private reasons and may or may not schedule a coinciding meeting.
Others: Also, many visitors don't see the president at all but rather meet with a Cabinet officer or some other official.