House of Islam vs Dar al-Islam

House of Islam and Dar al-Islam both are nouns.

Word	Noun	Adjective	Verb	Adverb
House of Islam	Yes	No	No	No
Dar al-Islam	Yes	No	No	No

As nouns, House of Islam and Dar al-Islam are synonyms defined as:

House of Islam and Dar al-Islam: areas where Muslims are in the majority

House of Islam (noun)	Dar al-Islam (noun)
areas where Muslims are in the majority	areas where Muslims are in the majority