This image (http://kardsunlimited.com/wp-content/uploads/2014/02/dawncake.jpg) is saved as 24 bit jpg and have 51340 unique colors.

After resize (dawncake_res.png - 1st in 1st row) it have 14570 unique colors (used as SOURCE).
\-After paste to MSPaint (dawncake_res_paste_to_MSPaint_C1_pal.bmp - 2nd in 1st row) it have 213 unique colors (without dithering!).
\-After import palette (dawncake_res_IrfanView_C1_pal_import.bmp - 3rd in 1st row) in IrfanView (with dithering) it have 126 unique colors.

When we reduce source image to 256 colors MSPaint palette (dawncake_res_256_colors_MSPaint_pal.bmp - 1st in 2nd row) we have 133 unique colors, but still need conversion to C1.
\-After paste to MSPaint (dawncake_res_256_colors_MSPaint_pal_paste_to_MSPaint.bmp - 2nd in 2nd row) we have 91 unique colors.
\-After import palette (dawncake_res_256_colors_MSPaint_pal_IrfanView_C1_pal_imported.bmp - 3rd in 2nd row) in IrfanView (no dithering this time, since source have less than 256 colors) we have 91 unique colors too - exactly same result.

So as we can see any method give more unique colors when source image have more unique colors (of coure there is other software where result can be even better).

Note: C1 *menu* palette is used in this example.

Made by QTZ.