I mean I know that with each color you have to use different emotions to access them but does each have a different power? Or do they all just have the powers of the green lantern?

different powers too. wikipedia tells you some powers

so what is white emotion and does it hint to something else...

The powers are generally the same: flight, energy constructs, etc. but have unique qualities.
 
Blue Lanterns can heal,  augment hope as well as a Green Lantern's power, but a Blue Lantern needs a Green Lantern to be around for theirs to work to full potential. they can also reverse the effects of a Red Lantern's Power Ring. No Batteries required, either.
 
The Orange Lantern Power Ring can absorb the power of other Lanterns' rings except Blue Lantern Rings and possibly Indigo Rings. The Orange Power ring can also create energy constructs of beings it has killed.
 
Indigo Power Staffs can turn power against other Lanterns and can combine lights to take out Black Lanterns
 
Black Lantern Rings can reanimate the dead, read emotions and regenerate hosts
 
Red Lanterns can sense anger/rage, can live without a heart, and fire this plasma like energy from their mouths (gross), plus the ring gives a big power boost, but if a Red Power Ring is removed, the user will die as the energy replaces blood except if it is removed by a Blue Lantern. 
 
Violet Rings can sense love (aww, that's nice) and can put people in suspended animation and read people's deepest desires
 
Green Lanterns and Yellow Lanterns have essentially the same abilities but Yellow Lanterns have a slight resistance to Green Lantern Rings