The cistern to which people will come and the river of al-Kawthar
Question

What is the cistern to which people will come? What is the difference between it and the river of al-Kawthar?
Praise be to Allah.The cistern to which people will come (al-hawd al-mawrud) is a cistern in the land of gathering which will belong to the Prophet (blessings and peace of Allah be upon him) on the Day of Resurrection. Al-Kawthar is a river in Paradise from which two spouts will pour water into this cistern which Allah has promised to His Prophet (blessings and peace of Allah be upon him), to which the believers of his ummah will come. It is a huge cistern, the length and width of which are the distance of a month’s travel. The believers will come to him, and whoever drinks one draught from it will never thirst again after that. Its vessels are as numerous as the stars of the sky, and its water comes down from Paradise, from the river of al-Kawthar. These are the details of this matter.
The cistern will be on earth and its water will come from Paradise. Al-Kawthar is a river in Paradise, and its water will come down into this cistern via two spouts, as the Prophet (blessings and peace of Allah be upon him) said: “They will pour into this cistern on the Day of Resurrection, and those who believe in Muhammad (blessings and peace of Allah be upon him) will come to it.”
What is meant by earth here is the land of the gathering. The river exists in Paradise at present, because Allah, may He be exalted, says (interpretation of the meaning): {Indeed, We have granted you, [O Muhammad], al-Kawthar} [al-Kawthar 108:1]. It is a mighty river in Paradise from which, on the Day of Resurrection, two spouts will lead to the earth which, on the Day of Resurrection, will be changed and the people will be standing on it.
(End quote from Shaykh `Abd al-`Aziz ibn Baz (may Allah have mercy on him): Fatawa Nur `ala ad-Darb, 1/356)