You cannot impose copyright or trademark on t-shirt designs. It is for the company's logo, brand name, company slogan/title, etc. And they only provide protection in the specific industry policies that they formulate. So, there are various companies that use the same brand name or slogan.

However, if they belong to different industry sectors it is unlikely that they are going to baffle the consumers with similar names. Treadmark is protecting your brand or company that someone can’t come in your way and feed off your success in the name of your brand by fooling people to buy a similar product as you sell.

Now, copyright is all about a publication like books, novels, etc.

In practical terms, you will have to file a copyright suit before the court for infringement or plagiarism. However, as per the judgments of the previous courts, they do not find T-shirts as a legit means of publishing items. And it is not strong enough to warrant a copyright.