Welcome to the wonderful world of gamma-correction and sRGB colorspace.

Your 122 in a [0 .. 255] range is 0.4784 in a [0.0 .. 1.0] range. But these values are gamma-corrected (more accurately, sRGB-corrected) , and correspond to 0.19462 of the “linear light”. In other words, if you display (122,122,122) on your screen, this emits 19.46% of the light you would get if you displayed pure white (255,266,255).

So 0.19462 + 0.19462 = 0.38924 (which is a “linear light” value) and if you compute the corresponding gamma/sRGB-corrected value you get 0.65705 which is 168 in your friendly [0 .. 255] range.

Of course, if the image has a color profile which is not sRGB, I assume that Gimp will take this in account as well.

Some more explanations and experiments on all this here.

A table of sRGB ⟺ Linear conversions: sRGB.ods (58.4 KB)

The available blend modes seem to be the same as the layer blend modes - some cause a different output, some do not e.g. ‘replace’ gives same result as ‘normal’. Somewhere I have a page showing a formula for each mode.