Difference between "place" and "position"
Solution 1:
A good way to think of it is that a position is more defined than a place: given the chess board example, the position a piece can be in is defined by the 64 squares on the board. While you could say the knight piece is in the place of A-4, it'd be more definitive to say it is in the position of A-4, to imply that there is structure to where it can be.
On the other hand, a place is more ambiguous and requires no structure.