What are the differences between respiration and photosynthesis ?

The two are
opposite ends of the same scale.

Photosynthesis is used to collect energy
from the sun and store it as chemical energy in sugar.  Respiration releases this stored energy
and uses it for other things e.g. movement. 

Photosynthesis chemical
equation: `6CO_(2)+6H_(2)O ->C_(6)H_(12)O_(6) + 6O_(2)`
Respiration Chemical
equation: `6O_(2)+C_(6)H_(12)O_(6)->6CO_(2)+6H_(2)O`

Plants and plankton
carry out both Photosynthesis and respiration, Other living things carry out only respiration. 
Organisms that carry-out photosynthesis are producers.  Organisms that only carry-out
respiration are consumers. 

I hope this helps.