Difference between the quaternion and the Euler angle rotation

ReadOnlyAttrib.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class ReadOnlyAttribute : PropertyAttribute
{

}

ReadOnlyDrawer.cs

using System.Collections;
using System.Collections.Generic;
using UnityEditor;
using UnityEngine;


[CustomPropertyDrawer(typeof(ReadOnlyAttribute))]
public class ReadOnlyDrawer : PropertyDrawer
{
	public override float GetPropertyHeight(SerializedProperty property,
		GUIContent label)
	{
		return EditorGUI.GetPropertyHeight(property, label, true);
	}

	public override void OnGUI(Rect position,
		SerializedProperty property,
		GUIContent label)
	{
		GUI.enabled = false;
		EditorGUI.PropertyField(position, property, label, true);
		GUI.enabled = true;
	}
}

rotation.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public enum RotationType {Quaternion, Euler};

public class rotation : MonoBehaviour {

	[Range(0.0f, 1.0f)]
	public float step = 0.0f;
	public RotationType type = RotationType.Quaternion;
	[ReadOnly]
	public Vector3 interpolated;

	static private Vector3 origin	{ get { return new Vector3 (0.0f, 0.0f, 0.0f); } }
	static private Vector3 x		{ get { return new Vector3 (1.0f, 0.0f, 0.0f); } }
	static private Vector3 y		{ get { return new Vector3 (0.0f, 1.0f, 0.0f); } }
	static private Vector3 z		{ get { return new Vector3 (0.0f, 0.0f, 1.0f); } }
	static private Vector3 start	{ get { return new Vector3 (0.0f, 90.0f, 0.0f); } }
	static private Vector3 end		{ get { return new Vector3 (90.0f, 45.0f, 90.0f); } }

	// Use this for initialization
	void Start () {
		
	}
	
	// Update is called once per frame
	void Update () {
		interpolated = (step * end + (1 - step) * start);

		switch(type) {
		case RotationType.Quaternion:
			inter_quaternion ();
			break;
		case RotationType.Euler:
			inter_euler ();
			break;
		default:
			throw new UnityException ();
		}
	}
		
	void inter_quaternion() {
		this.transform.eulerAngles = start;
		this.transform.RotateAround (origin, x, 45.0f * step);
	}

	void inter_euler() {
		this.transform.eulerAngles = origin;
		this.transform.RotateAround (origin, x, interpolated.x);
		this.transform.RotateAround (origin, y, interpolated.y);
		this.transform.RotateAround (origin, z, interpolated.z);
	}
}