Laravel : Search with posted parameters

I am new to Laravel so please be patient with me.

i have to implement search functionality in Laravel. i am able to send form data to the search controller and receiving it as well

public function search_results(Request $request){
        if ($request->has('gender')) {
           echo $request->gender;
        }
        .....
}

Now when i am following tutorials on the web i am getting such examples :

public function filter(Request $request, User $user)
{
    // Search for a user based on their name.
    if ($request->has('name')) {
       $user->where('name', $request->input('name'))->get();
    }

}

or

public function index()
{
    $users = User::where('status', 1)
                ->where('is_banned', 0)
                ->get(['name']);
    
    dd($users);
}

now i am not sure from where this User:: or User $user is being added, and what should i do in my scenario.

Your suggestions would be helpful ..

Thanks

via Chebli Mohamed