Since absolute potential isn't defined for a point, we take a reference point which is $\infty$, and then define potential of a point $A$ to be the work done per unit charge to move that charge from $\infty$ to that point. Moreover potential difference between two points $A$ and $B$ is the work done per unit charge to move that charge from $A$ to $B$. Now comes the case of battery and circuit. I have a series of doubts on this.
There are two ends of a battery $+,-$. And we say that these two have a potential difference. But i can't understand how to relate it with the definition i just leaned above. Here there is no electric field and we are not moving any charge from $\infty$ to those points. So analogy of the above with these small two points inside a small battery doesn't seem to click in my mind. Furthermore let's join that battery with a circuit with no resistance. What do we mean by all points in the circuit have equal potential?How do we relate it with the definition of potential above?Does it mean work done to bring a per unit positive charge from $\infty$ to that point in the circuit? Even if it is then which charge?Also,what does positive charge mean?Does it mean protons?
I have spent lion's share of high school physics in solving text book problems related to current and static electricity but didn't get to understand the very basics of these things and how to relate those. We were just taught how to apply formula to solve problems. Please help clear out my basics, respected physics lovers.