Next we have a Hadith from Sahih Muslim:
Book 5, Number 2265:
Hamza b. 'Abdullah b. Umar heard his father cay that the Messenger of Allah (may peace be upon him) had said: The person would continue begging from people till he would come on the Day of Resurrection and there would be no flesh on his face.
Here we see that begging would cause a terrible punishment on the Day of Resurrection. But what does Abu Huraira say? Here is the Hadith immediately following...
Book 5, Number 2266:
Abu Huraira reported Allah's Messenger (may peace be upon him) as saying: He who begs the riches of others to increase his own is asking only for live coals, so let him ask a little or much.
Abu Huraira says it is ok to "ask" if it is just a little. Is trying to get others to recite the Qur'an with the goal of receiving charity a good thing or a bad thing? Seems like begging.
Actually if you knew rhetoric, you would realise that Abu Hurairah (ra), or rather the Prophet (pbuh), is using irony in the second hadith. The Prophet (pbuh) said that whoever begs the riches of others to increase his own is asking only for live coals, so let him ask a little or much in reference to the live coals. Who is going to ask for little or much coals? Nobody. It is called irony.
Besides, begging is asking when you have something. This is how the Prophet (pbuh) explained the difference between begging and asking:
Imam Ahmad recorded that Abu Sa`id said, "My mother sent me to the Messenger of Allah to ask him for help, but when I came by him I sat down. The Prophet faced me and said to me,
Â«مَنِ اسْتَغْنَى أَغْنَاهُ اللهُ، وَمَنِ اسْتَعَفَّ أَعَفَّهُ اللهُ، وَمَنِ اسْتَكَفَّ كَفَاهُ اللهُ، وَمَنْ سَأَلَ وَلَهُ قِيمَةُ أُوقِيَّةٍ فَقَدْ أَلْحَفÂ»
(Whoever felt satisfied, then Allah will enrich him. Whoever is modest, Allah will make him decent. Whoever is content, then Allah will suffice for him. Whoever asks people, while having a small amout, he will have begged the people.)
Abu Sa`id said, "I said to myself, `I have a camel, Al-Yaqutah, and indeed, it is worth more than a small amount.' And I went back without asking the Prophet for anything.'' This is the same wording for this Hadith collected by Abu Dawud and An-Nasa'i.
Thus there is nothing wrong with asking, nor is asking considered begging, from an Islamic perspective. Begging is when you have something, even if little, and you still ask. Had actually Abu Hurairah (ra) asked for food, it wouldn't have been called begging. He was eligible to ask because he had nothing in Madinah during a certain period.