Actual photons?

One of the allures of amateur astronomy is to say that we're seeing
the "actual photons" from pick your favorite deep sky object. I was
thinking about this and wondering about the veracity of this
statement. Since most of us use reflectors or refractors with a
diagonal, I was wondering if it is the *same* photon that gets
reflected off of a mirror. Since I am scientifically challenged, I
don't know the answer. I also don't know if the question even makes
sense (is there such a thing as "sameness" in the quantum mechanical
world?).