These methods work correctly, you just have to take into account effects of anti-aliasing and rounding.
First, turn on anti-aliasing to see everything (not only rounded result):
graphics.SmoothingMode = SmoothingMode.AntiAlias;
Now FillRectangle(10,10,10,10) will produce blurry result and DrawRectangle(10,10,10,10) will be sharp.
The blurry result means that you have pixel coordinates off-grid. If you need to call:
graphics.FillRectangle(9.5f, 9.5f, 10, 10);
to align top-left corner of the rectangle on grid.
The DrawRectangle is sharp because it uses Pen of width 1.0. So the line starts on the pixel center and goes 0.5 pixels in both directions, thus filling exactly 1 pixel.
Note that width and height are computed this way:
width = (right - left) = 19.5 - 9.5 = 10
height = (bottom - top) = ...
Notice that 19.5 is a right/bottom coordinate of the rectangle also aligned on the grid and the result is a whole number.
You can use different formula:
width2 = (right - left + 1)
But this applies on rounded coordinates only, since the smallest unit is 1 pixel. When working with GDI+ that uses anti-aliasing, be aware of the fact that the point has zero size and lies in the center of pixel (it is not the whole pixel).