I have a whole subsection of one folder devoted to "Parting Songs", many of which mention "a parting glass": many have lines or phrases in common with each other. so, not surprisingly, their origins sometimes get confused, and/or "Which song are you talking about?"

I have heard the "Frank Harte" song which Bob linked to above being described as Irish, probably because he and Cathal McConnell are known for singing it. Its usual title is "When First we Met" and is by English songwriter, Alan Bell. And it's in the DT under that title.

As for Sheila's song, I was taught it as "Kind Friends and Companions" - again using the first line as title, and it does then distinguish it from other "Parting Glass" songs. The tune is shared by a number of other songs - not such an unusual scenario in folk music - apart from "Lovely Molly" there's "Puir Roving lassie". You can't keep a good tune down!