carefreeness vs cheerfulness

carefreeness and cheerfulness both are nouns.

Word	Noun	Adjective	Verb	Adverb
carefreeness	Yes	No	No	No
cheerfulness	Yes	No	No	No

As nouns, cheerfulness is a hypernym of carefreeness; that is, cheerfulness is a word with a broader meaning than carefreeness:

Other hypernyms of carefreeness include blitheness.

carefreeness (noun)	cheerfulness (noun)
the trait of being without worry or responsibility	the quality of being cheerful and dispelling gloom
the cheerful feeling you have when nothing is troubling you	a feeling of spontaneous good spirits