atan2(vector1.y - vector2.y, vector1.x - vector2.x)

is the angle between the difference vector (connecting vector2 and vector1) and the x-axis, which is problably not what you meant.

The (directed) angle from vector1 to vector2 can be computed as

angle = atan2(vector2.y, vector2.x) - atan2(vector1.y, vector1.x);

and you may want to normalize it to the range [0, 2 π):

if (angle < 0) { angle += 2 * M_PI; }

or to the range (-π, π]:

if (angle > M_PI)        { angle -= 2 * M_PI; }
else if (angle <= -M_PI) { angle += 2 * M_PI; }

(x > 0 ? x : (2*PI + x)) * 360 / (2*PI)

Atan takes single argument and Atan2 takes two arguments.The purpose of using two arguments instead of one is to gather information on the signs of the inputs in order to return the appropriate quadrant of the computed angle, which is not possible for the single-argument Atan

Atan2 result is always between -pi and pi.

Reference: https://en.wikipedia.org/wiki/Atan2