If you want a solution that fits both scenarios go into Image-> adjustment and chose black and white, and fiddle with the setting till you get the result you want. Or you can use hue/saturation and drag the saturation slider all the way to the left. The first option gives more control over the conversion, the other is just faster.
You can also chose image -> adjustment -> desaturate it will IIRC work the same way as hue / sat.
If you merely desaturate the image, which is what many people do, you will get an image in which all equally saturated colors become equal grays - regardless of their hues, or their effect on human perception.