The old-time collectors who wandered the countryside in the late 19th C and into the 20th focussed on themes and floating verses. Two songs could have different melodies or many different words, but if they were on the same topic or shared floating verses, they tended to lump them. They even lumped them if they were in entirely different languages. Then they gave the group a name like The False Knight or The Two Sisters.

This makes sense if you are interested in songs as literature, but it's not much help to a person who wants to make music.

There's a sad old lyric with the words "o waly, waly" in the chorus. There's another one that starts "The water is wide, I cannot cross o'er." And just because these two songs share some lines, the collectors also gave "The Water is Wide" the name "Waly Waly".

Does that make sense? No. The songs have different melodies, mostly different words, and one has a chorus and one does not. I personally think that O Waly, Waly is more naive and countrified than The Water Is Wide.

A good way to see the music is to go to abcnotation.com and do two searches.

waly, waly
Water is wide

Some extraneous tunes which happen to have those words will come up to irritate you, and then quite a few versions of the tune you want will also come up. For "The Water is Wide," I like #19, which is in 4/4 time.