Hello!
A few months ago, I saw a video on YouTube called Sailor Moon theories. I don't know how to post videos on here, but it's about 22 minutes long and was created by trueedge2097. I strongly suggest you watch the video, since this was originally his theory and I've simply expanded on it.
Anyway, one of the first things he addresses is the existence of Sailor Moon in the Silver Millenium. His theory was that Queen Serenity was the Sailor Moon of that time. The reasons he puts forth are that she is able to use the Moon Stick and The Silver Crystal. This also explains why Luna and Artemis would have remembered Sailor Moon and Princess Serenity as different people.
"But," you may be asking, "Why were the Inners princesses of their planets?" Well, (and I'm also not sure how to put spoilers yet) as we see in the Dream arc, the Inner Senshi during the Silver Millenium were older than Princess Serenity. So, my conculsion is that if Princess Serenity had not died, than eventually she would have become Saior Moon. Thanks for reading this!