The biggest difference between photosynthesis and respiration is that photosynthesis only occurs in plants and some bacteria while respiration occurs in all living organisms. They do share one big similarity and that is that the process of photosynthesis is actually the same process only it is completed in reverse.
Photosynthesis is Carbon Dioxide and Water that, through the process, yield Glucose and Oxygen.
Respiration is Glucose and Oxygen that, through the process of respiration, yield Carbon Dioxide and Water.
The two work well together because living organisms supply plants and some bacteria with the carbon dioxide needed to undergo photosynthesis, and plants and some bacteria give off oxygen which living organisms need to breathe or respire.