The last Hadith used the word ﴿Salah﴾ `prayer' in reference to reciting the Qur'an, (Al-Fatihah in this case) just as Allah said in another Ayah,

﴿وَلاَ تَجْهَرْ بِصَلاتِكَ وَلاَ تُخَافِتْ بِهَا وَابْتَغِ بَيْنَ ذَلِكَ سَبِيلاً﴾

(And offer your Salah (prayer) neither aloud nor in a low voice, but follow a way between.) meaning, with your recitation of the Qur'an, as the Sahih related from Ibn `Abbas. Also, in the last Hadith, Allah said, "I have divided the prayer between Myself and My servant into two halves, a half for Me and a half for My servant. My servant shall have what he asked for.'' Allah next explained the division that involves reciting Al-Fatihah, demonstrating the importance of reciting the Qur'an during the prayer, which is one of the prayer's greatest pillars. Hence, the word `prayer' was used here although only a part of it was actually being referred to, that is, reciting the Qur'an. Similarly, the word `recite' was used where prayer is meant, as demonstrated by Allah's statement,

﴿وَقُرْءَانَ الْفَجْرِ إِنَّ قُرْءَانَ الْفَجْرِ كَانَ مَشْهُودًا﴾

(And recite the Qur'an in the early dawn.Verily, the recitation of the Qur'an in the early dawn is ever witnessed.) in reference to the Fajr prayer. The Two Sahihs recorded that the angels of the night and the day attend this prayer.