Whats the difference between these two quaternions ?

Whats the difference between

Code (csharp):

1. Quaternion.AngleAxis(0, Vector3.up)

and

Code (csharp):

1. Quaternion.AngleAxis(15, Vector3(0, 0, 0))

Are they both valid and what happens if they are not ?

 

Both are valid, but they don't really do anything.

The first one rotates 0 degrees around the up vector.
Vector3.up is the same as writing Vector3(0,1,0) btw;

The second one rotates 15 degrees around the zero vector, which also is the same as no rotation at all

 

I ask because I want to rotate and move my object toward some other object. But I don't want to use LookAt() becase I want to rotate smoothly.
This code works but when direction changes to next object (waypoint) my object continues just forward with no change in direction, or sometime it does but not towards next object but in some random direction.

This is my code:

Code (csharp):

1.         distance = waypoints[next].position - transform.position;
2.         if(distance.magnitude < epsilon)
3.             next = PickWaypoint(next);
4.        
5.         rotationDir = Vector3.Cross(transform.forward, distance.normalized);
6.         rotationDir.Normalize();
7.         angle = Vector3.Angle(transform.forward, distance.normalized);
8.         rotation *= Quaternion.AngleAxis(angle*Time.deltaTime, rotationDir);
9.        
10.         transform.rotation = Quaternion.Slerp(transform.rotation, rotation, damping*Time.deltaTime);
11.         transform.Translate(new Vector3(0.0f, 0.0f, 1.0f)*Time.deltaTime*speed);