In my sets, I'm likely to sing a combination of 'stuff'. I'll likely include a couple of ballads like 'Lady Margaret' and/or 'Come All You Fair & Tender Ladies', then shift to Old-Time music - 'Handsome Molly' for example. I'll also include 'Hesitation Blues' or 'Delia' because I love blues and ahve played them for years. Then maybe throw in some Richard Thompson, John Prine, or Dar Williams song that fits the mood. And I almost never play an evening without singing "Love Hurts" and "The Dark End of The Street" because I am always effected in a positive way by singing them.
So, some of it's folk and some of it's not. But I like all of it.
If someone asks what kind of music I play, I usually say old songs. If they press for more information, we can talk about blues and folk and old time country and what they mean. And the person I'm talking with probably goes away with a completely different concept of those terms than I hold in my head and heart.
As others in this discussion have stated, the distinction really shouldn't be about labels, but about quality and sincerity. Or something like that, anyway.