Joker traces the origin story of Arthur Fleck, a troubled man (mentally, financially, and in several other ways) who goes into a downward spiral and emerges as a maniacal killer. My question: is Arthur Fleck the Joker we see in other Batman movies (e.g. Heath Ledger's Joker)? Nothing in the movie seems to confirm this, and - as far as I know - no Batman movie/comic book/etc gives the real name of the Joker. We see at the end of the movie that Arthur (who was introduced as Joker on Murray Franklin's show) starts some sort of movement against the elite of Gotham, and people inspired by him and his actions dress up as Jokers and riot around the city. Is it not entirely plausible that the real Joker is just someone inspired by Arthur, and not Arthur himself?
An example that shows that this theory is not inconsistent with other representations of the Joker: In Dark Knight, when we're first introduced to Ledger's Joker in a bank robbery scene, the other people robbing the bank with him don't seem to know much about him or his name. One of them even describes him as "some guy who calls himself Joker". If this Joker is indeed Arthur Fleck - who became infamous after his appearance on Murray Franklin's show - how is it that these people don't know anything about him?