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)

Answer

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

Answer

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

Bye!
Xavi

Evden çıkmadan dil öğrenme fırsatını kaçırmayın. Deneyimli dil eğitmenlerimizden oluşan seçkimize göz atın ve ilk dersinize şimdi kaydolun!