ʿAbd al-Walī is a person whom Allah has made a walī (friend of God) from among the righteous (ṣāliḥ) and the believers (muʾmin). Allah says: He watches over all His righteous servants. Allah is the friend (walī) of those who have iman (faith); He turns towards His awliyāʾ (friends) from among His righteous and believing servants with His walāya (friendship/protection). (Kāshānī, 120; Jāmiʿ, 10)
ʿAbd al-Ẓāhir is the one who is ẓāhir (manifest) through acts of obedience and goodness. Thus, he has discovered Allah through His Name al-Ẓāhir (the Manifest). In this way, he understands that He is the Manifest.