From the Bury website:
We are delighted to announce that a team of Bury legends will be gracing the Gigg Lane pitch to take on a Burnley legends team.
This is match organised by the Bury Supporters Association who are seeking to resurrect the original Bury FC team.
A pheonix club already exists Bury AFC. Bury AFC is currently a member of the North West Counties Football League Division One North and won the 2021–22 division championship, earning promotion to the league's Premier Division for the 2022–23 season.
They are an entirely different entity.