asthma vs respiratory illness

asthma and respiratory illness both are nouns.

Word	Noun	Adjective	Verb	Adverb
asthma	Yes	No	No	No
respiratory illness	Yes	No	No	No

As nouns, respiratory illness is a hypernym of asthma; that is, respiratory illness is a word with a broader meaning than asthma:

asthma: respiratory disorder characterized by wheezing; usually of allergic origin
respiratory illness: a disease affecting the respiratory system

Other hypernyms of asthma include respiratory disease, respiratory disorder.

asthma (noun)	respiratory illness (noun)
respiratory disorder characterized by wheezing; usually of allergic origin	a disease affecting the respiratory system