Puff and popcorn stitches are similar in looks, but quite different in the making.
While popcorn stitches are a ‘bunch of stitches bundled together’, puff stitches are made by a ‘bunch of yarn overs’.
Due to their construction, puff stitches often look neater on their ‘wrong side’ and might need to be ‘popped’ forward if they are supposed to show up on the side on which they have been made.
Both stitches have one thing in common: they can easily be adapted in size by either making more double crochets or trebles (popcorn stitch) or more yarn overs (puff stitch).
They tend to use up quite a bit of yarn, especially compared to simpler and flatter stitches, but the effects can be great with either stitch.
The advantage of puff stitches over popcorn stitches is that ‘puffs’ can be worked quicker than ‘popcorns’ and that they look ‘smoother’ (if that is what someone is looking for).