No surprise, you�ve got it backwards, kinda . . .
Conventional current flow was determined before they actually knew which way current flows. It was though it flowed the other direction from the �greater (positive)� to the �lesser (negative)� potential.
Current is mostly due to the direction of flow of electrons which actually move from the previously thought �negative� toward the �positive� potentials. The reverse 'negative' and 'positive' designations have been retained in spite of this error because these labels were already in wide use when the error was discovered.
To add to the confusion, less prevalent ionic current flow IS from �positive� to �negative�. The conventional current flow is still the norm widely used so that the maths add up correctly.
I'll check back later when I've finished verifying my 'facts'.