The Gabriel hadith describes Islam through the profession of faith, prayer, almsgiving, fasting Ramadan, and pilgrimage when able. An objection follows: if Islam is described through actions, how can it be united with inward faith?
The response distinguishes the pillars and outward signs of Islam from a claim that its entire religious reality consists only of physical acts. Describing a religion through its obligations does not settle the technical definition of genuine submission.
The separate instructional questions concerning Islam and faith clarify different aspects, but a teaching distinction need not entail complete theological separation.