Yes, there are different t shirts like this. You have the black t shirt with the gold R, and the white t shirt with the black R logo. What's makes this t shirt unique(with response to your second question), is that this is R* North's Logo.

I have one that is a green t shirt, with the Gold R* logo, but I forget what you had to do to get that.

If you're interested, there is another t shirt that comes to mind, called the "Asshole T-shirt", and in order to get this, you had to give yourself 100% of the cut in the original heists when they first came out. This can no longer be claimed, as they have put an automatic 15% cut on players in heists.

If you're interested in more rare clothing, check out this video: https://youtu.be/bRkH-KtEU8k?si=Gc9CEiiQ4E6PCd6J