How to find adjacent points in a 3D space in c++

I have a couple of points in a 3D space, and I want to write a condition to determine whether two points are adjacent: are they only a single unit apart in the integer lattice?

I have a struct named Point that holds x,y and z coordinates. Then in the main function, I set the values for points a,b,c,d,e and push them into a vector. Then in the for loop I want to check if two points are adjacent or not. Currently I'm just checking if they are on the same axis, but I do not know how to proceed.

struct Point {
   int x;
   int y;
   int z;
};
bool adjacent(Point a, Point b) { ??? }

int main() {
    struct Point a = {0, 0, 0};
    struct Point b = {0, 0, -1};
    struct Point c = {1, 0, -1};
    struct Point d = {1, -1, -1};
    struct Point e = {2, -1, -1};

    assert(adjacent(a, b));
    assert(adjacent(b, c));
    assert(adjacent(c, d));
    assert(adjacent(d, e));
    assert(!adjacent(a, c));
}

By adjacent I mean something like in this photo:

Very briefly:

for each pair of points:
    if two of the three coordinates are equal AND
              the other coordinate differs by 1:
        then mark the pair as adjacent.

Iterating through point pairs is simple enough: the first point a walks through indices 0-(n-2); the second point b walks through indices from a's position through the end, n-1.

Checking adjacency is also easy, given integer coordinates.

diff = abs(a.x - b.x) + 
       abs(a.y - b.y) + 
       abs(a.z - b.z)

diff = 1 iff the points are adjacent.