In Boolean algebra, the sum refers to the XOR operation. This makes sense to me because in GF(2) the sum is supposed to implement a sum modulo 2, which has the same truth table of the XOR logical operation.
However, in the context of sum of products, the sum refers to the logical OR operation, which is used to combine the logical ANDs representing the terms in a logical expression. Why is the sum used to represent different operations in different contexts, and how are these different meanings related to each other?