On both holidays, it starts off with a short paragraph, beginning with the words for which it is named.
After that, each holiday has a unique paragraph, describing the events for which that day is celebrated.
Probably the first to explicitly mention the words "Al HaNissim" is Rabbi Achai Mishbaha in the She'iltot and its full version is found for the first time in the order of Rabbi Amram Gaon and Siddur RSG.
Various rabbis endorsed the recitation of Al Hanisim on Yom Ha'atzmaut, and even penned unique versions of this prayer, although this practice is not universally accepted.
The first to publish a version of Al Hanisim for Yom Ha'atzmaut was Rabbi Ezra Zion Melamed.