"winmail.dat" attachments sent to Mac Mail received differently from two separate Mac email addresses.

Microsoft implemented their own scheme with Exchange Server and Outlook.

It seems that this usually works better in more recent versions, so this may also be an older or unsupported Exchange Server or Outlook configuration, or a configuration or a user that's been expressly set to send TNEF files. Or Microsoft and the folks running Exchange Servers are getting better about the defaults for external email traffic. (The numbers of TNEF questions being posted around here has been dropping off.)

Your choices here...

Use one of the available TNEF tools to decode the messages.

Or do what we do around here for various questions, and ask for details of the client's specific system and specific email client, and then send them screen-shots of how to set up a foreign recipient. It's arguably the Exchange Server that's misconfigured for sending to foreign users, but that's not all that unusual.

Per a Microsoft TNEF-related web page, assuming not-ancient Exchange Server and Outlook client versions, and assuming Windows...

Change the format of all new messages

On the File tab, choose Options > Mail.

Under Compose messages, in the Compose messages in this format list, click HTML, Plain Text, or Rich Text.

Here, select HTML.

That same Microsoft web page has how to select the recipient settings for the older Outlook 2010 client, if that's what this user is running.

What is confusing to me is that when such attachments are sent to two separate email addresses which are setup identically via a Google email server and received via Mac mail, one email has the attachment as “winmail.dat” (which must then be opened via a third party application) and the other email address automatically shows the attachment in it’s original format, whether it’s a PPT file, JPEG image or Word document.

Mac mail preferences show that both email addresses have been setup identically except for the actual name in the address field. Is there a solution here that I'm missing?

Such things are not always easily explained away.

If your email contains a winmail.dat attachment - Apple Support

So you're wondering why two different addresses work differently, where one receives winmail.dat files and the other receives typical MIME-encoded attachments directly visible using Apple Mail? The most likely explanation is that the sender of one is marked as local in Exchange Server, and the other is marked as foreign. within the Exchange Server configuration. Or that the sending user has marked one address as foreign, and not the other. (See the Microsoft TNEF docs for settings and options.) Or the receiving mail server for one is an Exchange Server, and it's configured for TNEF and for foreign access. The less likely explanation is that some other receiving email server is unpacking the TNEF bits on your behalf. Or ask the folks at Microsoft. This is their mess, after all.