You’re correct - there are two (or more) theories, and the direction of flow doesn’t matter:
“Electron Flow Theory” states that current flows from negative to positive.
“Conventional Flow Theory” states that current flows from positive to negative.
The direction of Electron flow is from Negative potential to Positive potential. As electrons vacate their atoms, during electron flow, positively charged atoms (with Holes) result. The flow of electrons in one direction causes a flow of positive charges (holes) in the opposite direction. This flow of positive charges is known as “Conventional Current Flow”
All of the effects of Electron Flow (from Negative to Positive) are exactly the same as those that would be created by a Conventional Current flow in the opposite direction. The two conventions are essentially equivalent, and may be consistently used interchangeably - as all predicted effects will be the same.
And then there’s “Hole Theory” -vs- “Smoke Theory” debate: