Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
Firstly:
Both a gift and charity involve giving money to others without compensation. However, the difference between them is that a gift is intended to foster affection towards the recipient, whereas charity is solely for the sake of reward and drawing closer to Allah, regardless of the recipient.
Shaykh Al-Islam Ibn Taymiyyah (may Allah have mercy on him) said:
"Charity is what is given for the Face of Allah, as pure worship without any specific person in mind, nor seeking any benefit from them; rather, it is placed where charity is needed, like for those in need.
As for a gift, it is intended to honor a specific person; either out of love, friendship, or to fulfill a need… When this is understood: charity is superior unless there is a meaning in the gift that makes it better than charity: like giving to the Messenger of Allah (peace and blessings be upon him) during his life out of love for him. And like giving to a relative to uphold family ties, or to a brother for the sake of Allah: this may be better than charity." End quote from "Majmu` al-Fatawa" (31/269).
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
"Know that giving money voluntarily can be a gift, a present, or charity. What is intended for the reward of the Hereafter in itself is charity, what is intended for affection and reconciliation is a gift, and what is intended for the benefit of the giver is a present (Hibah). This is the difference between them, and affection and reconciliation are intended by the Shari`ah and aimed for the reward of the Hereafter, but the reward of the Hereafter is not the primary intention, and for this reason, it is specified for a particular person. As for charity, it is not specified for a particular person, but any poor person encountered is given, and all have in common that it is a pure donation for which the giver asks nothing in return." End quote from "Ash-Sharh Al-Mumti`" (11/65).
Secondly:
Ongoing charity is what a person gives in charity, and its reward continues for him after his death as long as it is being benefited from, and for this reason, scholars have explained it as an endowment, because it is what continues to be benefited from for a long time; thus, the reward continues for the one who endowed it.
Al-Manawi (may Allah have mercy on him) said in "Fayd al-Qadir" (1/602):
"Ongoing charity is that which continues after him, like an endowment." End quote with adaptation.
And Qadi `Iyad (may Allah have mercy on him) said in "Mashariq Al-Anwar" (1/281):
"(Or ongoing charity) means: its benefit and reward continue and last." End quote.
And Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
"Ongoing charity is that which continues to be benefited from, and for this reason, it is called ongoing, because it does not stop.
Non-ongoing charity is that which is only benefited from at its time.
For example: If you give a poor person a thousand riyals, which he spends in a month or two; the charity ends.
But if you endow a building, a house, or a shop, to have its revenue go to the poor: then the charity is ongoing as long as its revenue exists. Printing books and beneficial things is ongoing charity, as long as people benefit from them, it is ongoing in reward, ongoing in merit." End quote.
Thus, a gift is not considered ongoing charity, as it is enjoyed for a limited period, then it disappears and ends.
Please see the answer to question no. (122361 ).
Therefore, a gift is not considered ongoing charity, as it is enjoyed for a limited period, then it ceases and ends.
Thirdly:
What appears is that what you give to your poor aunt is charity, not a gift, because you give it to her due to her need and poverty. However, the matter depends on your intention and purpose; it is possible to intend a gift for your relative, despite her need; otherwise, as long as you give it for the sake of need and intend by that to draw closer to Allah, it is charity.
Charity to relatives is better than to others, as it carries two rewards: the reward of charity and the reward of upholding family ties.
The Prophet (peace and blessings be upon him) said: "Charity given to a poor person is charity, and to a relative, it is two things: charity and upholding family ties." Narrated by An-Nasa’i (2582) and authenticated by Al-Albani.
Fourthly:
If you give your parents money as a token of love for them, it is a gift, and its reward is immense, as it falls under being dutiful to parents, which is one of the greatest righteous deeds.
It has been previously explained that charity, although superior to a gift in principle, a gift may be better than it if it is for a close relative, as upholding family ties, along with the gift, may have a greater reward than charity to someone distant.
And there is no closer kinship than that of parents; so upholding ties with them through gifts and the like is from the great dutifulness towards them.
For benefit, please see the answer to question no. 34614
If your father then donates this money to build a mosque or something else, the basic principle is that the reward is for him, as the money became his property by your gifting it to him.
Nevertheless… it is hoped for you to have goodness and reward, and that you share in the reward, because you were the cause of him donating this money.
The Grace of Allah is vast, and no worker's reward is lost with Him.
And Allah knows best.