The Executive Committee is the group of people directly responsible to see that the functions of the convention are successful and handled well. They may act individually or together, and they may have a staff to assist with the detailed work. However, these people are the prime decision makers at the highest convention organization level. A lot of conventions run with "an executive committe of one", and call that position the Chair.
The chair or executive committee is responsible for managing the rest of the convention staff, including choosing (and removing if necessary) department, division, or area heads (whatever the people at the next management level down from the top are called).
Many conventions are organized as corporations. As such, they typically have corporate officers such as a President or Chief Executive Officer, a Treasurer or Chief Financial Officer, a Secretary or Archivist, and so on, like any Board of Directors.
Alternatively, for instance if a convention is run by a club, there may be a parent corporation that provides legal shelter for the convention but does not get involved in the detailed organization or implementation of the convention other than to approve the Chair, or the budget, or the theme/Convention Committee, etc. Some groups have bid cycles to determine who is running a convention for a particular year, where proposals are brought to the Board. Other groups have popular elections to determine the ConChair and/or Guests of Honor.
Even if there is a separate parent corporation with a President and Treasurer, every convention must have its own Treasurer as well. It is also advisable for every convention to have an Vice Chair, so that there is a clear path of authority should the ConChair be unavailable or have to step down (Real Life Happens, you know). The Vice Chair can also have other convention responsibilities, but they should be light enough at-con to allow the Vice Chair to relieve the ConChair and give them a break at some point.