When we are thinking about the same piece of memory in multiple different times, would the corresponding brain activities always be the same? Or how similar/different can the corresponding brain activities be?
The term for the brain activity that corresponds to an experience is "neural representation".
Neural representations "drift" over time. From https://elifesciences.org/articles/51121:
Similar ‘representational drift’ has been shown in other neocortical areas and hippocampus (Attardo et al., 2015; Ziv et al., 2013; Levy et al., 2019).
So that means that the brain activities corresponding to an experience can change over time.