The difference between sprinkling water and washing is that sprinkling is merely splashing water onto the site of the impurity (najasah).
Other reports explain what is meant by sprinkling: “Water should be splashed on the urine of a baby boy, and the urine of a baby girl should be washed.” Narrated by Ibn Majah, 525; classed as authentic (sahih) by al-Albani.
Imam al-Haramayn said: The scholars said that sprinkling means covering the impurity with a lot of water, but not to the point that the water soaks it.
End quote from Al-`Iddah fi Sharh al-`Umdah, by Ibn al-`Attar, 1/185.
Az-Zarqani (may Allah have mercy on him) said: In linguistic terms, the word nad-h (translated above as sprinkling) may mean splashing water onto something or pouring water onto it.
End quote from Sharh az-Zarqani `ala al-Muwatta’, 1/249.
As for washing, it means making the water flow over something until it covers it and runs off it, but it is not necessary to wring it out.
Ibn al-Mulaqqin said: Sprinkling means making the water reach everywhere there is urine, but it is not stipulated that the item should be submerged and water be allowed to run off it. This is indicated by the words: then he sprinkled water on it and did not wash it.
Washing means submerging something in water and lifting it out of it, and it is not stipulated that one should wring out the garment in this case.
End quote from Al-I`lam bi Fawa’id `Umdat al-Ahkam, 1/681.
It says in Minhat al-`Allam: The difference between washing and sprinkling is that washing means submerging an item in water and lifting it out and letting the water drip from it. In the case of sprinkling, it is not stipulated that one should submerge the item then lift it up and let the water drip from it; rather it means sprinkling a lot of water on it, but not to the point that water drips from it.
End quote from Minhat al-`Allam fi Sharh Bulugh al-Maram, 1/124.
From this it will be clear that the extra factor in washing is that the water runs through the garment, which is submerged in the water, then lifted out and the water drips from it. As for sprinkling, it means simply splashing the water onto the site of the impurity until it is soaked, but the water does not need to flow or drip from the garment after it is sprinkled or splashed with water.
When washing, there is no need to wring out the water by hand from the site of the impurity; rather it is sufficient simply to let the water drip from it by itself.
An-Nawawi (may Allah have mercy on him) said: It is not stipulated, in order to purify a garment, that one should wring it out, according to the more correct view.
End quote from Rawdat at-Talibin, 1/28.
Khalil (may Allah have mercy on him) said: If the site of the impurity is washed with pure water, and the water drips from that place, there is no need to wring it out, because of the general meaning of the hadiths.
End quote from Mawahib al-Jalil, 1/163.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: Is wringing required after removing the impurity itself?
He replied: Wringing is not required, unless removal of the impurity depends on that, such as if the impurity had penetrated the washed item, and the inside of it cannot be cleaned except by wringing, in which case it must be wringed out.
End quote from Fatawa Nur `ala ad-Darb by al-`Uthaymin, 7/2.
For more information regarding the scholarly difference of opinion about the ruling on wringing out impurity (najasah), see: Mawsu`at at-Taharah by Abu `Umar ad-Dubyan, 13/525-528.
See also the answer to question no. 239096.
And Allah knows best.