It does seem to be similar to a puff stitch, I found an antique pattern (believed to be public domain) at http://www.antiquepatterns.dreamhosters.com/HegeChild.pdf
Here is my transcription of the instructions for the bean stitch.
The bean-stitch is made thus: (Thread over, insert hook in space, draw thread through to length of a treble) 8 times, over and draw through all the loops at once, over and draw through the stitch remaining, tightly, to close the cluster. ("Child's Crocheted Bonnet with Star Crown," Hege, W. C., Needlecraft, March 1916, Vol. 7)
Noted differences is the number of repeats and length of the loops drawn up. ([YO], insert hook in same [base stitch], draw up a loop to length of a treble) 8 times, YO and draw through all loops on hook, ch 1, tightly, to close cluster.
Since throughout that pattern, the author uses ch 4 and then treble to start each round I believe it is the US treble. The length of the loops in this bean stitch are made to match that the other stitches in the round. The number of repeats could be required because the pattern uses crochet thread ("number 10 or number 15") or to make it a more pronounced and fuller shape. (more like a bean.)
NexStitch describes a Puff stitch as 3 to 5 HDC cluster in same base stitch, and a chain to close tightly. I read two alternate finishes on eHow: Alternate 1, Make a single crochet stitch to finish off the puff stitch; Alternate 2, pull the yarn through 5 [sic] of the 7 loops on your hook, then YO and draw through last 2 [sic]loops on your hook. (**Note if you pull through 5 of 7 loops on hook then you will have three loops to pull through after the YO, so one of numbers is incorrect.) :roll:
So I'd say the puff and the bean stitches are similar with a puff being fewer repeats of the HDC in the cluster (all in same base stitch at the bottom and drawn together at the top at the finish. Whereas the Bean stitch would be more repeats and closed tightly with a following ch st.
The instructions you linked would give a sc + 2 hdc cluster (6 loops) closed tightly with a following ch st.
Puff (3 to 5 HDC cluster)
Bean (6 to 8 HDC cluster, pulled tight with ch)