It is often said that if a point A has a potential higher than a point
B, then A has a positive potential and B a negative potential.
All the statement means is that the potential at A is higher than B so that the potential difference $V_{A}-V_{B}$ is greater than zero. The terms negative potential and positive potential have no meaning by themselves. The potential at a point is always relative to some other point.
Is it forcibly concluded that a point with a positive potential is
positively charged, or that a point with a negative potential is
negatively charged?
No.
Consider two negatively charged objects. Object 1 has a negative charge of 1 coulomb. Object 2 has a negative charge of 2 coulombs. The potential of object 1 is higher than object 2 because it is more "positive", yet object 1 is negatively charged.
Hope this helps.