First, a little about definitions.
Orbital states can be described with several terms:
Filled - An orbital that contains the maximum number of electrons it can hold.
Empty - An orbital that contains no electrons.
Occupied - An orbital that contains at least one electron.
Unoccupied - An orbital that contains at least one open space for an electron.
With these definitions in mind, we can see that a filled orbital is also occupied, but an occupied orbital is not necessarily filled. Also, an orbital can be both occupied and unoccupied. A good way to remember this is that occupied means that one space is occupied by an electron, and unoccupied measn at least one space is free to accept an electron. Thus, it is better to think of filled and empty in terms of the entire orbital, but of occupied and unoccupied in terms of the spaces for electrons.
So, the best way to remember the terms would be as follows:
Filled - An orbital that is filled with the maximum number of electrons it can hold.
Empty - An orbital that is empty of electrons.
Occupied - An orbital that has at least one space occupied by one electron.
Unoccupied - An orbital that has at least one unoccupied space for an electron.
So, turning now to Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO), we can understand what is meant by these terms better with our definitions form above. These orbitals are called the frontier orbitals, and determine the way the molecule interacts with other species. The HOMO is the orbital that could act as an electron donor, since it is the outermost(highest energy) orbital containing electrons. The LUMO is the orbital that could act as the electron acceptor, since it is the innermost(lowest energy) orbital that has room to accept electrons. In accordance with the above definitions, a single orbital may be both the LUMO and the HOMO.