"Did the singer distinguish at all between these songs/that kind of song and those which had an earlier origin"
Sorry Blackie - you're obviously a newcomer here

Yes - he most certainly did, and spoke at length about the differences
The Irish Travellers were the same
There is every suggestion that many source singers did
I've quoted this many times, but this differentiation was summed up perfectly by Jeam Richie describing when she was recording in Ireland in the early fifties:
From an interview repeated a few years ago in The Irish Times

"“I used the song Barbara Allen as a collecting tool because everybody knew it.
When I would ask people to sing me some of their old songs they would sometimes sing ‘Does Your Mother Come from Ireland?’ or something about shamrocks.
But if I asked if they knew Barbara Allen, immediately they knew exactly what kind of song I was talking about and they would bring out beautiful old things that matched mine, and were variants of the songs I knew in Kentucky. It was like coming home.”

"I meant to ask, is that Alvar Liddell BBC broadcaster?"
Yes, it was Nick - he befriended Phil Tanner some time before he was recorded"
There is an unconfirmed story that Tanner was recorded by a 'Dialect Society' group who were studying the local dialects in South Wales and they recorded most of his songs, but the recordings were never made available because the songs never fell within the remit of The Society

I know for sure that Linguaphone recorded both Welsh and Scots language traditional songs on cylinder for their projects and that copies of those are housed at C# House - we have copies of them - poor condition, but interesting
Jim