The hadith you mentioned was referenced in several hadiths' books, and it is authentic (sahih). Using Sunnan Ibn Majah 5/1448:
حَدَّثَنَا أَحْمَدُ بْنُ مَنْصُورِ بْنِ سَيَّارٍ، حَدَّثَنَا عُثْمَانُ
بْنُ عُمَرَ، حَدَّثَنَا شُعْبَةُ، عَنْ أَبِي جَعْفَرٍ الْمَدَنِيِّ،
عَنْ عُمَارَةَ بْنِ خُزَيْمَةَ بْنِ ثَابِتٍ، عَنْ عُثْمَانَ بْنِ
حُنَيْفٍ، أَنَّ رَجُلاً ضَرِيرَ الْبَصَرِ أَتَى النَّبِيَّ (ﷺ) فَقَالَ
ادْعُ اللَّهَ لِي أَنْ يُعَافِيَنِي. فَقَالَ "إِنْ شِئْتَ أَخَّرْتُ
لَكَ وَهُوَ خَيْرٌ وَإِنْ شِئْتَ دَعَوْتُ". فَقَالَ ادْعُهْ.
فَأَمَرَهُ أَنْ يَتَوَضَّأَ فَيُحْسِنَ وُضُوءَهُ وَيُصَلِّيَ
رَكْعَتَيْنِ وَيَدْعُوَ بِهَذَا الدُّعَاءِ "اللَّهُمَّ إِنِّي
أَسْأَلُكَ وَأَتَوَجَّهُ إِلَيْكَ بِمُحَمَّدٍ نَبِيِّ الرَّحْمَةِ يَا
مُحَمَّدُ إِنِّي قَدْ تَوَجَّهْتُ بِكَ إِلَى رَبِّي فِي حَاجَتِي
هَذِهِ لِتُقْضَى اللَّهُمَّ فَشَفِّعْهُ فِيَّ ".
It was narrated from 'Uthman bin Hunaif that a blind man came to the
Prophet (ﷺ) and said: "Pray to Allah to heal me." He said: "If you
wish to store your reward for the Hereafter, that is better, or if you
wish, I will supplicate for you." He said: "Supplicate." So he told
him to perform ablution and do it well, and to pray two Rak'ah, and to
say this supplication: "Allahumma inni as'aluka wa atawajjahu ilaika
bimuhammadin nabiyyir-rahmah. Ya Muhammadu inni qad tawajjahtu bika
ila rabbi fi hajati hadhihi lituqda. Allahumma fashaffi'hu fiya (O
Allah, I ask of You and I turn my face towards You by virtue of the
intercession of Muhammad the Prophet of mercy. O Muhammad, I have
turned to my Lord by virtue of your intercession concerning this need
of mine so that it may be met. O Allah, accept his intercession
concerning me)".
The blind man asked the Prophet (ﷺ) to pray for him to be healed, as the supplication of the Prophet (ﷺ) is more likely to be answered due to his stance.
The Prophet (ﷺ) advised the blind man that it is better to have patience, but the Prophet (ﷺ) still offered to supplicate for the blind man at the time. The blind man elected to have the supplication at the time, so the Prophet (ﷺ) supplicated for him, and taught him the words for supplication with intercession:
O Allah, I ask of You and I turn my face towards You by virtue of the
intercession of Muhammad the Prophet of mercy.
The Prophet (ﷺ) here shows the blind man that all supplication should be to Allah (see Qur'an 40:60), and he asks Allah to accept the supplication of the Prophet (ﷺ) (by virtue of the intercession of Muhammad), which the blind man had already specified before (Pray to Allah to heal me). The power of intercession is only for Allah to grant (see Qur'an 43:86), hence the supplication was to Allah (O Allah, I ask of You and I turn my face towards You) to accept the intercession.
O Muhammad, I have turned to my Lord by virtue of your intercession
concerning this need of mine so that it may be met.
This is a form of politeness: to let the Prophet (ﷺ) know that the blind man was thankful for the intercession (supplication) of the Prophet (ﷺ), and that the blind man had also supplicated likewise. There is no supplication in this statement; merely information.
O Allah, accept his intercession concerning me.
The blind man then turned to Allah one more time asking Him to accept the intercession (supplication) of the Prophet (ﷺ).
In other words, the hadith revolves around supplication:
- Directly by the blind man, supplicating for himself to be healed.
- As an intercession by the Prophet (ﷺ), supplicating for the blind man to be healed.
To the best of my knowledge, we have no further information of what happened to the blind man afterwards.
The reasoning for the choice of words will be mere speculation, since there is no verse or hadith that inform us otherwise. Most likely, as mentioned earlier, the blind man knew that the stance of the Prophet (ﷺ) was much higher than his, and that the chances of his supplication being accepted were higher if the supplication came directly from the Prophet (ﷺ). The Prophet (ﷺ) taught the blind man the words to use to supplicate that the intercession by the Prophet (ﷺ) be accepted. Since the Prophet (ﷺ) is dead, and we can no longer ask him to supplicate on our behalf, we only have the option of his teachings to follow when performing supplication as per his hadith in Riyad as-Salihin:
إذا صلى أحدكم فليبدأ بتحميد ربه سبحانه، والثناء عليه، ثم يصلي على
النبي صلى الله عليه وسلم ثم يدعو بعد ما شاء
When any one of you have performed Salat (prayer) and wants to
supplicate, let him praise Allah first then glorify Him in the
beginning and then he should supplicate Allah for me. Then he may
supplicate for whatever he likes.
