Both the bracket operator [] and the .at(i) function can be used to access elements in an array or vector, but they have key differences in functionality. The .at(i) method includes bounds checking, which means it will throw an out_of_range exception if the index i is outside the valid range of the vector's size. In contrast, the [] operator does not perform any bounds checking, potentially leading to undefined behavior if an out-of-bounds index is accessed. This distinction is crucial for ensuring safe access to array elements in programming.