Does canciones infantiles mean both children's songs and nursery rhymes?
Or is there another word for nursery rhymes?

Question

Answer

Se les puede decir: - Canciones infantiles
                                   - Canciones de cuna
                                   - Arrullo

Answer

"Canciones infantiles" means "children"s songs". https://www.youtube.com/watch?v=m8GN0bWWmrs

"Canción de cuna" and "nana"" are "lullaby"." https://www.youtube.com/watch?v=H3YFEwQoAjs

Answer

If I am not wrong, "nursery rhymes" can be:
"rimas infantiles" (poemas)
"canciones infantiles" (songs for children)
"canciones de cuna" (songs for babies)

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Hi Dawna, as far as I know "nursery rhyme", or "lullaby", is "canción de cuna".

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Hi Dawna! 
You're right 'Canciones infantiles' means 'Children's songs'.

Bye!
Xavi

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