It is not uncommon for animes to have samples of previous OPs in later seasons or to reuse OPs from older productions of the same anime. But I have found no examples of 2 different animes having the same OP. After some research to confirm this, I found some rumors of D-gray man and Shakugan no shana sharing the same OP Light my fire, but I was not able to confirm this as none of the seasons of D-gray man have it listed as an OP. So, while it is posable for 2 different animes to share an OP I can’t find any examples. The reason that it is unlikely is because of copywrite laws. When a company uses a song, they have to pay royalties to the writer and preformer/s. When another company wants to use the same song they have to get permission from first company as well as paying royalties so it can get really complicated until a song enters public domain which usually takes 25 years and even after it has, any new versions or covers by other performers or companies fall under the same copywrite laws.