Is fractional coordinates same as reduced coordinates while describing the coordinates of atoms in a crystal lattice?

The OCTOPUS code for TDDFT describes in its manual:

ReducedCoordinates: the position of the atoms inside the unit cell, in reduced coordinates.

It mean that the independent coordinates of all the atoms in the given unit cell will be between 0 and 1.

However, in the description of ReducedCoordinates OCTOPUS page also mention that: Note that in Octopus the origin of coordinates is in the center of the cell, so the coordinates inside the cell are in the range [-0.5, 0.5).

Does this statement imply that I should input the fractional coordinates such that everything must be in the range [-0.5,0.5)?. This definition contradicts the very definition of fractional coordinates! Or is it something that internal only to the OCTOPUS code?

What am I missing here?

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