Istisqa supplication asks not merely for rain in quantity but for beneficial relief without harm. A reported phrase is:
اللَّهُمَّ اسْقِنَا غَيْثًا مُغِيثًا
Translation: O Allah, grant us rain that brings relief.
Ghayth connotes needed rain and mughith rain that relieves distress. These particular words are not a condition for the prayer’s validity.