The Executive and the Assembly are not the same!
The Assembly is the legislature, or law-making body, made up of MLAs elected by the people of Northern Ireland to represent their views and make laws on their behalf. It meets in the Assembly Chamber of Parliament Buildings, in the grounds of the Stormont Estate in Belfast.
The Executive is the government of Northern Ireland, made up of Ministers in charge of Government Departments. It meets in Stormont Castle, not too far away from Parliament Buildings, also on the Stormont Estate.