unity control problem

I built an first person shooter with the problem, that the controls just change the position of my game object on the normal xyz-axis.

That is very confusing for the player. How is it possible to change the position of the game object with the same input-keys but with the camera xyz-axis?

My code so far:

 using UnityEngine;
 using System.Collections;
 
 [RequireComponent(typeof(Rigidbody))]
 public class PlayerBehaviour : MonoBehaviour
 {
     [System.Serializable]
     public class MoveSettings
     {
         public float runVelocity = 12;
         public float rotateVelocity = 100;
         public float jumpVelocity = 8;
         public float distanceToGround = 1.3f;
         public LayerMask ground;
     }
 
     [System.Serializable]
     public class InputSettings
     {
         public string FORWARD_AXIS = "Vertical";
         public string SIDEWAYS_AXIS = "Horizontal";
         public string TURN_AXIS = "Mouse X";
         public string JUMP_AXIS = "Jump";
     }
 
     public MoveSettings moveSettings;
     public InputSettings inputSettings;
 
     public Transform spawnPoint;
 
     private Rigidbody playerRigidbody;
     private Vector3 velocity;
     private Quaternion targetRotation;
     private float forwardInput, sidewaysInput, turnInput, jumpInput;
 
     bool Grounded()
     {
         return Physics.Raycast(transform.position, Vector3.down, moveSettings.distanceToGround, moveSettings.ground);
     }
 
     void Awake()
     {
         velocity = Vector3.zero;
         forwardInput = sidewaysInput = turnInput = jumpInput = 0;
         targetRotation = transform.rotation;
         playerRigidbody = gameObject.GetComponent<Rigidbody>();
     }
 
     void Start()
     {
         GameData.Instance.Lives = 3;
         Spawn();
     }
 
     void Update()
     {
         GetInput();
         Turn();
     }
 
     void FixedUpdate()
     {
         Run();
         Jump();
     }
 
     void GetInput()
     {
         if (inputSettings.FORWARD_AXIS.Length != 0) forwardInput = Input.GetAxis(inputSettings.FORWARD_AXIS);
         if (inputSettings.SIDEWAYS_AXIS.Length != 0) sidewaysInput = Input.GetAxis(inputSettings.SIDEWAYS_AXIS);
         if (inputSettings.TURN_AXIS.Length != 0) turnInput = Input.GetAxis(inputSettings.TURN_AXIS);
         if (inputSettings.JUMP_AXIS.Length != 0) jumpInput = Input.GetAxis(inputSettings.JUMP_AXIS);
     }
 
     void Run()
     {
         velocity.z = forwardInput * moveSettings.runVelocity;
         velocity.x = sidewaysInput * moveSettings.runVelocity;
 
         velocity.y = playerRigidbody.velocity.y;
 
         playerRigidbody.velocity = transform.TransformDirection(velocity);
     }
 
     void Turn()
     {
         if (Mathf.Abs(turnInput) > 0)
         {
             targetRotation *= Quaternion.AngleAxis(moveSettings.rotateVelocity * turnInput * Time.deltaTime, Vector3.up);
         }
         transform.rotation = targetRotation;
     }
 
     void Jump()
     {
         if (jumpInput != 0 && Grounded())
         {
             playerRigidbody.velocity = new Vector3(playerRigidbody.velocity.x, moveSettings.jumpVelocity, velocity.z);
         }
     }
 
     public void Spawn()
     {
         transform.position = spawnPoint.position;
     }
 
     void OnTriggerEnter(Collider other)
     {
         if (other.gameObject.tag == "DeathZone")
         {
             OnDeath();
         }
     }
 
     void OnCollisionEnter(Collision other)
     {
         if (other.gameObject.tag == "Enemy")
         {
             Enemy enemy = other.gameObject.GetComponent<Enemy>();
             Collider col = other.gameObject.GetComponent<Collider>();
             Collider mycol = this.gameObject.GetComponent<Collider>();
             if (enemy.invincible)
             {
                 OnDeath();
             }
             else if (mycol.bounds.center.y - mycol.bounds.extents.y > col.bounds.center.y + 0.5f * col.bounds.extents.y)
             {
                 GameData.Instance.Score += 10;
                 JumpedOnEnemy(enemy.bumpSpeed);
                 enemy.OnDeath();
             }
             else
             {
                 OnDeath();
             }
         }
     }
 
     void JumpedOnEnemy(float bumpSpeed)
     {
         playerRigidbody.velocity = new Vector3(playerRigidbody.velocity.x, bumpSpeed, playerRigidbody.velocity.z);
     }
 
     void OnDeath()
     {
         GameData.Instance.Lives--;
         Spawn();
     }
 }