Question

what are the horizontal and vertical parts of vectors called

Answer 1

A 2-dimensional vector may be expressed by 
A = Ax i + Ay j
where i and j are unit vectors along the x (horizontal) and y (vertical) axes respectively.
Ax =  horizontal part (x-component)
Ay = vertical part (y-component)

Alternatively, the vector may be written as
A = (Ax, Ay)

Answer: 
Horizontal part = x-component
Vertical part = y-component