“I ask You and turn to You by means of Your Prophet Muḥammad, the Prophet of mercy.”
That is: through his supplication and his intercession—exactly as ʿUmar said, “We used to seek a means to You through our Prophet.” In both ḥadīths, therefore, the terms “tawassul” (seeking a means) and “tawajjuh” (turning) carry the same meaning.
He then said, “O Muḥammad, O Messenger of Allah, I turn with you to my Lord concerning my need that He may fulfil it. O Allah, let him intercede for me.” In other words, he asked Allah to accept the intercession of His Prophet on his behalf.
His words, “O Muḥammad, O Prophet of Allah,” and the like, are simply a form of address meant to keep the one addressed present in the heart. One speaks to this inward vision just as the worshipper, while praying, says: “Peace be upon you, O Prophet, and the mercy of Allah and His blessings.” People do this often, addressing someone they envision inwardly even though no one outwardly hears the speech.
Thus, the expressions “seeking a means through a person,” “turning through him,” or “asking by him” are ambiguous and multilayered. Those who did not grasp the Companions’ intent were misled by this. The phrases may mean seeking a means through him because he prays and intercedes, or because the supplicant responds to him, obeys his command, and follows his example. The causal link, then, is either the supplicant’s love for him and his adherence to him, or the Prophet’s own supplication and intercession.
Alternatively, they may be understood as swearing an oath by him and seeking a means through his very person, so that the tawassul involves neither something he does nor something the supplicant does, but solely his person—or simply invoking him as an oath upon Allah. It is this second understanding that they rejected and forbade, and the same is true of phrases such as “asking by something …”