Are those who have believed—whom Allah and His Messenger mention—those who have perfectly embraced Islam, or could their submission be incomplete?

The phrase "those who believe" or "the believers" applies to those with complete faith, or to those who possess the fundamental principle of faith. This includes a general belief that the Qur’an is the word of Allah, the last of the revealed books, an enduring proof, abrogating what preceded it and superseding it, and that its accounts must be believed and its rulings obeyed. This is in addition to a general belief in the authentic Sunnah (definition) of the Prophet. Whoever believes in this is considered among "those who believe."