Barms were made with dough made using beer froth, similar to this bread:
<a class="postlink" href="http://www.bbc.co.uk/blogs/food/2011/07/the-ale-barm-method-worthy-of.shtml" onclick="window.open(this.href);return false;">http://www.bbc.co.uk/blogs/food/2011/07 ... y-of.shtml</a>
Muffins were made using left over bread dough from yeasted bread, which would have been made with a sourdough starter even at the beginning of the industrial revolution then with commercial yeast from around the turn of the 19th century.
Once yeast was available commercially and available in blocks from 1825 and more widely available from 1867 it became too much of a faff to make bread using the barm method. So the recipes were altered to have yeast in them and barms , in effect, became a different, lighter textured variety of muffin.
You can still make barms with beer froth, however they are rarely available commercially. Those things that are sold as barms are a lighter form of MUFFIN. Sotoday's excuse for a barm is actually a MUFFIN and MUFFINS are never barms.
Also: Bread types made with Barm has it's origin in Celtic peoples, hence 'barm brack' in Ireland. Sourdough was introduced by the Romans.
barm mortuus est, vivat muffin
(the barm is dead, long live the MUFFIN)