how and why do objects appear different in coloured light

Colors of object are the colors of white light they reflect, when a white light fall a blue object al other color is absorb while the blue part of the light is reflected and the object depict that color.

Object appear differently in coloured object because of color combination, when blue light  fall on green object it appears cyan because the blue light from the object combine with the  green light we apply( remember the green color is part of white light reflected by the object) and vice versa .  When red light fall on green object, the green and red combine to form yellow  ( remember the green on the object is part of the white light reflected by the object) and vice versa.

Therefore object under white light depict the color they reflect while object under colored light depict the color they combine with.