I have heard it applied to all of those- related songs by one composer, I believe, was the original meaning. Examples: Sir Arnold Bax, "A Celtic Song Cycle." (One I have and enjoy).
A dictionary definition: A group of songs, unified musically or textualy. It was popular with Germans and those who copied the idea, so the word lieder may be added to the above. The German word is Liederkreis, used by Schumann.
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sj