Hello I have a question:

Question

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.

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?

Potential talks about potential difference. You cannot just have potential, it is not like energy. We can define a potential difference between two points using the elementary definition: $$V = V(A) - V(B)$$ In the case of $$V(A)>V(B)>0$$, you can say there is positive potential even though charges at points A and B are both positive. There is a convention we use in physics where we can talk about the potential of simply one charge alone. However, as before, we need a reference point. You can never talk about potential without analyzing the difference between two points. When we talk about the potential of one charge alone, it is usually assumed that $$V=0$$ at $$\infty$$. In this case, the only way to have negative potential is if the lone charge is negative. If the lone charge is positive it has positive potential.

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.