How can I save the high score for a 2D game

Question

I have a script that doesn't save the high score automatically and before I put the restart button my high score was saved without any code. I want the high score to be saved even if the player restarts the game .This is my code for the SCORE:

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

public class Score : MonoBehaviour
{
    public int score;
    public Text ScoreText;
    public int highscore;
    public Text highScoreText;


    void Start()
    {
        highscore = PlayerPrefs.GetInt("HighScore: " + highscore);
    }

    void Update()
    {
        ScoreText.text = "Score: " + score;
        highScoreText.text = highscore.ToString();
        if (score > highscore)
        {
            highscore = score;

            PlayerPrefs.SetInt("HighScore: ", highscore);
        }
    }
    void OnTriggerEnter(Collider other)
    {
        Debug.Log("collider is working");
        if (other.gameObject.tag == "Score: ")
        {
            score++;
        }
    }
}

And this is the code for the restart button:

using UnityEngine;
using UnityEngine.SceneManagement;
using System.Collections;

public class RestartGame : MonoBehaviour
{
    public void RestartsGame()
    {
        SceneManager.LoadScene(SceneManager.GetActiveScene().name); // loads current scene
    }
}

Answer 1

You have problems with the keys used by PlayerPrefs:

void Start()
{
    highscore = PlayerPrefs.GetInt("HighScore");
}

void Update()
{
    ScoreText.text = "Score: " + score;
    highScoreText.text = highscore.ToString();
    if (score > highscore)
    {
        highscore = score;

        PlayerPrefs.SetInt("HighScore", highscore);

    }
}