"Lights Switched" toggles the cell selected and its immediate orthogonal neighbours.
"Lights On Diagonally" does exactly the same except that diagonal neighbours are toggled on or off, ie, if a neighbour is on it is turned off.

Select an "N x N" grid size to display that grid for examination.

Offer a lowest switching sequence for each grid (for the 3 x 3 it takes 5).