Is the displacement always equal to distance covered in a linear motion? What is a linear motion? If a stone is thrown vertically and it reaches the ground following the same path, is it undergoing linear motion?

No ,Linear motion (also called rectilinear motion) is a motion along a straight line, and is also called one- dimension motion. No, Displacement is not always equal to distance in one dimension(linear motion), because let us understand with help of an example
A man walks starting from origin in (+)ve x-direction 12 metres and come backs to its initial position , here displacement=final position – initial positon = 0 as, he came back to its original position. but total distance = actual path length = 12+12 metres= 24 m . If, the man starting from his initial position do not come to the origin then, displacement of man= distance of man=12 m

 

If a man throws a stone vertically upwards then it is 2 dimension motion as both x and y- coordinate changes with time