GoDaddy uses cPanel last I recall, so their servers have a functional mail server already installed and setup. When an e-mail is sent from your domain on their servers, it can be validated.
When you send e-mail from your Droplet that may not have a functional e-mail server setup to validate outgoing mail, it lands in junk/spam as the receiving server can't verify that it's being sent from the intended sender/domain(s)/host.
WordPress, without a plugin, sends mail using PHP's
mail() function which doesn't validate what's being sent, or who's sending it. It sends what you tell it, when you tell it.
There's two ways to fix that. The first would be to setup a working mail server on your Droplet and go through the process of setting up Postfix, SPF, DKIM, DMARC, and PTR (Reverse DNS).
If you go this route, this will get you started, but it's not all-inclusive and there's still much of what I noted above that needs to be installed and configured beyond what this guide details:
The second and, in my opinion, better method would be to use a transactional e-mail provider such as SparkPost, SendGrid, or Mailgun (all of which have WordPress plugins to integrate with their API).
Using the above, you're not managing a mail server on your own (which can be a major pain, if you're not sure what you're doing) and SparkPost allows you to send up to 100,000 e-mails per month, which should fit most users needs.