'Fluffy' suggests air and lightness. Typical objects that are fluffy to touch are a thick, soft towel or bathrobe. A little chick is fluffy when it's a few days old. You can beat egg whites until they're fluffy to make a cake or pancake which is light and airy. 'Puffy' is generally more negative. Something which is puffy appears swollen. For example, if you have an allergic reaction to something, your eyes might look puffy.

I also think the difference could be visual/tactile. Something that is puffy could be inflated to a larger size, but I associate fluffiness with softness. For example, an airbag in a car is puffed up to a large size, but is not necessarily soft. It is inflated and the fabric is very tight around the enclosed air. A pillow, or a scarf, or a furry jacket may not be big in size but can be fluffy and soft. Some types of chips, are described as 'puffed' for example 'cheese puffs' -- but they are actually pretty crunchy when you bite them. Something puffed would seem to describe its size. Hope this was not too confusing! Feel free to ask me follow up questions!

Fluffy: Adjective A cat can be very fluffy because of its fur. Puffy: Adjective A body part can be puffy (eyes). "My eyes are so puffy today" or Puffy white clouds or A puffy snow jacket