Puffy eyes can mean that both the upper and lower eyelids look swollen. 'Bags' usually refer to pouches beneath the eyes - ie just the lower eyelids. Bags may be accompanied by dark shadows or 'troughs' beneath the lower eyelids.
To remedy this
* get enough sleep
* apply cool compresses to the eyes (Don't put ice directly on your skin!) Cold satin eye-masks can help. Put them in the fridge for a while before you use them.
* drink plenty of water
* avoid stress (meditation helps)
* Don't eat too much salt
* ask your doctor to check you for sinus problems or allergies