Square grid or offset rows
In a square grid, every plant sits the same distance from its neighbors in straight rows and columns. In offset rows, each row shifts by half a spacing and the rows sit closer together, 0.87 times the spacing, so each plant is still the full spacing from its neighbors. Offset rows usually fit more plants in a wide bed; in a narrow bed the count can be the same or lower.
Every plant sits at least half a spacing in from the edge of the bed, so its leaves stay inside the walls.
Where the spacing comes from
Use the spacing printed on your seed packet or plant label. The calculator counts plants for the spacing you enter; it does not choose a spacing for a crop. To fill the bed first, use the raised bed soil calculator; to water the rows, the irrigation fit checker.