Reason(s) why method runs when boolean is not set to an instance variable?

Question

I'm just starting Ruby and have a beginner question. Why is it that when pin_number == @pin (in the display_balance and withdraw methods), I get an error, but when I edit to set pin_number == pin, both methods then work?

In the methods below, I have the private class pin setting @pin = 1234, so I thought that should have worked using @pin and not pin.

class Account
  attr_reader :name, :balance
  def initialize(name, balance=100)
    @name = name
    @balance = balance
  end

  def display_balance(pin_number)
    if pin_number == @pin
      puts "Balance: $#{@balance}"
    else
      pin_error
    end
  end

  def withdraw(pin_number, amount)
    if pin_number == @pin
      @balance -= amount
      puts "Withdrew #{amount}. New balance #{amount}."
    else
      pin_error
    end
  end

  private
  def pin
    @pin = 1234
  end

  def pin_error
    return "Access denied: incorrect PIN."
  end
end

checking_account = Account.new("Rick", 1_000_000)
checking_account.display_balance(1234)

Answer 1

Below the methods, I have the private class pin setting @pin = 1234, so I thought that should have worked using @pin and not pin.

No; pin calls that method, which both sets @pin = 1234 and returns its value.

Referencing @pin just references that variable and nothing more; it does not invoke the private pin method.

I believe this should answer your other questions.