It's difficult to answer that in general. The main difference is probably that you can trust our clothes given by the GOTS certified manufacturer.
The fact is that every company can also create its own product seals. The criteria are self-set and usually adjusted very selfishly. Furthermore, entire marketing departments are often busy shaping their own image in a social and fair way through pseudo-green campaigns and projects. You have to consider that such expensive marketing concepts are often still cheaper than switching the entire value chain to green & fair.
If in doubt, you can ask the following question:
Would you assume that a company would set up its own sustainability label or invest enormous sums in 'greenwashing' if its own products could easily get an independent, well-known certificate?
Here
you can find a guide and here
a website focused on sustainable purchase advice.