Based on the information in Wikipedia - Chestnut Mushrooms and the answer located here at What are the mushrooms used in this (video) recipe? I would take an educated guess that since the chestnut mushroom is brown and not as fully matured (or big) as the portabella mushroom that it must be a baby portabella mushrooom, or the mushroom between a white mushroom and a portabella mushroom.

I am not entirely sure myself since there seems to be numerous aliases to these mushrooms and I can't seem to find a website that lists all the aliases to these mushrooms.