How to apply same script to only one game object at a time...

I'm fairly new to Unity and #C programming. I am creating a turn-based strategy game. Each team has a "commander" and nine units each. Every unit (including the commander) on each team is using the same script to move across the board. This script includes a "playerMoving" variable (bool) to pass into the animator scripts. When this variable is true, a running animation would play as the unit is moving across the gird. Unfortunately, because this script is attached to each unit, every unit's running animation will play even though only one is moving.

I tried creating different animation scripts for each unit and different animators for each unit, but that doesn't seem to solve the issue. It would appear that the issue would be in my "PlayerMove" script that is attached to every unit. How would I specify that only the current game object's playerMove variable should be set to true? Here is my PlayerMove script:

 public class PlayerMove : TacticsMove {

 GameObject target;
 GameObject aiUnit;
 GameObject playerUnit;
 public static bool playerMoving = false;
 public static bool playerAttacking = false;
 public static bool skipUnit = false;

 private static int attackCount = 0;

 // Use this for initialization
 void Start ()
 {
     Init();

     //Anim = GetComponent<Animator>;

 }


 // Update is called once per frame
 void Update()
 {
     Debug.DrawRay(transform.position, transform.forward);

     if (!turn)
     {
         return;
     }

     if (newUnitTurn)
     {   // Just got turn. Find path and start moving
         FindSelectableTiles(gameObject);
         CheckMouse();
         playerMoving = false;
         newUnitTurn = false;
         moving = false;
         NPCMove.NPCMoving = false;
         return;
     }

     if (moving)
     {   // Continue moving to target tile
         Move();
         playerMoving = true;
         NPCMove.NPCMoving = false;
         NPCMove.NPC_Attacking = false;
         return;
     }
     else
     {
         CheckMouse();
     }

     if (attacking)
     {
         playerAttacking = true;
         PlayerAttacksNPC(aiUnit);
         Debug.Log("Target unit; " + aiUnit);
     }

     if (skipUnit)
     {
         skipUnit = false;
         DontMove();
     }


 }

 // Check whether left mouse clicked. Here, if mouse click is on an enemy unit
 // in a reachable target, set playerAttacking flag.
 void CheckMouse()
 {
     NPCMove.NPCMoving = false;
     NPCMove.NPC_Attacking = false;

     bool skipUnit = false;
     if (Input.GetKeyDown("space"))
     {
         StartCoroutine(WaitTime(0.3f));
         skipUnit = true;
     }
     else if (Input.GetMouseButtonUp(0))
     {
         Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);

         RaycastHit hit;
         if (Physics.Raycast(ray, out hit))
         {
             Debug.Log("Mouse hit " + hit.collider.tag);
             if (hit.collider.tag == "Tile")
             {
                 Tile t = hit.collider.GetComponent<Tile>();
                 Debug.Log("Tile selectable " + t.selectable);
                 if (t.selectable)
                 {
                     moving = true;
                     MoveToTile(t);
                 }
             }
             else if (hit.collider.tag == "NPC")
             {   // Will attack NPC pointed by mouse click. 
                 Tile t = GetTargetTile(hit.collider.gameObject);
                 target = hit.collider.gameObject;
                 aiUnit = t.GetUnitObject();

                 // Calculate the distance if it is less than range start moving
                 float npcDistance = Vector3.Distance(transform.position, target.transform.position);

                 if (npcDistance < this.GetComponent<Unit>().GetRange() + 1)
                 {
                     moving = true;
                     willAttackAfterMove = true;
                     DontMove();
                 }
                 else if (npcDistance <= this.GetComponent<Unit>().GetMove() + this.GetComponent<Unit>().GetRange())
                 {
                     moving = true;
                     // Find next selectable tile from adjacency list aand move to it
                     willAttackAfterMove = true;      // Set player attacking mode
                     MoveToSelectableNeighborTile(t, this.GetComponent<Unit>().GetRange(), 
 this.gameObject);
                 }

             }
         }
     }
 }


 void PlayerAttacksNPC(GameObject aiUnit)
 {   // Player Attacks NPC pointed by mouse click
     //Debug.Log("Player attacking NPC........");
     //PlayerCombat.SetStats(soldier.Unit.GetAttack(), soldier.Unit.GetDefense, target.Unit.GetAttack(), target.Unit.GetDefense); FIX LATER*****
     PlayerCombat pc = new PlayerCombat();
     //pc.SetStats(5, 5, 5, 5);
     
     int dmg = pc.AttackPhase(true, this.GetComponent<Unit>().GetAttack(), this.GetComponent<Unit>().GetDefense(), aiUnit.GetComponent<Unit>().GetAttack(), aiUnit.GetComponent<Unit>().GetDefense());
     aiUnit.GetComponent<Unit>().TakeDmg(dmg);
     Debug.Log("Player hits for: " + dmg);
     Debug.Log("Player has: " + this.GetComponent<Unit>().GetHealth());

     attacking = false;
     willAttackAfterMove = false;
     StartCoroutine(WaitTime(1.0f));
     //Debug.Log("I done waited");
     //TurnManager.EndTurn();

     /* attackCount++;      // Increase attack count for testing
      if (attackCount < 5)
      {
          Debug.Log("Player hits for: " + dmg);
      }
      else
      {
          attackCount = 0;

          // Run following when attack completes for turning to another unit
          Debug.Log("Player attacks ended....Turning to another unit");
          attacking = false;
          TurnManager.EndTurn();
      }*/
 }

 IEnumerator WaitTime(float sec)
 {
     print(Time.time);
     yield return new WaitForSeconds(sec); //This Command doesn't get activated; why not?
        // Time.timeScale = 0;
     TurnManager.EndTurn(); //Supposedly it must be called from the CoRountinue what ever it is you want to happen
 }

 }

Here is my PlayerAnimator script:

   public class PlayerAnimController : MonoBehaviour {

 private Animator playerAnim;

 // Use this for initialization
 void Start () {
     this.playerAnim = this.GetComponent<Animator>();
 }
 
 // Update is called once per frame
 void Update ()
 {

     if (PlayerMove.playerMoving)
     {
         playerAnim.SetBool("Running", true);
     }
     else
     {
         playerAnim.SetBool("Running", false);
     }

     if (PlayerMove.playerAttacking)
     {
         playerAnim.SetBool("Attacking", true);
     }
     else
     {
        playerAnim.SetBool("Attacking", false);
     }

 }

 public void SetAttackingPlayer()
 {
     PlayerMove.playerAttacking = false;
 }
 }  

(I apologize for the line spacing).