Lake or Tarn?

This is the tea towel (see Monday) that led me to believe that Brothers Water was a "lake" in the Lake District.  The lakes on the tea towel are listed in order of size.
 
As I mentioned on Monday, the “Visit Cumbria” website has the same list but thinks Elter Water is the smallest "lake"  and has Brothers Water as a tarn.
 
BUT I have subsequently found that the Lake District National Park (LDNP) website, possibly more authoritative than the Visit Cumbria site , lists Brothers Water as a lake.  Although it strangely omits Elter Water completely  from its facts and figures section . 
 
Both sites and the tea towel seem to agree there are only 16 lakes in the Lake District so what is a tarn?  LDNP says “tarn” comes from the Old Norse tjörn meaning small mountain lake.  But what is small?
 
I have two books on the Tarns of the Lake District (extra) perhaps one of these can define a tarn and tell me what the difference is between a lake and a tarn.   No luck there. Neither mention Elter Water or Brothers Water.  The authors must agree these two bodies of water are too large to go in their book.
 
A listing of lakes and tarns on Wikipedia has Brothers Water being larger than Elter Water so I have concluded  the tea towel was right all along. I've geo tagged Elter Water for the Blip  because I geotagged Brothers Water on Monday. (Just in case anyone wondered where it was!)
 

And today Storm Agnes went through this part of the UK so I stayed indoors.