What type of polyester is most commonly used for clothing?
Based on several sources (shown below), it appears that polyethylene terephthalate (PET) is in fact used in the production of fabrics, including textiles. PET is marketed under names such as Dacron, Terelene, or Lavsan by various companies depending on your location. As to if it is the only textile polyester, I was unable to be completely certain. However, it appears to be a major textile polyester at the very least, as 39 million megagrams were produced in 2008 for fabrics alone.

Though it was not part of your question, I thought that I should include the following, as I found it interesting:

As it turns out, not only is PET used as a fabric, but it also makes a very nice fabric that is highly resistant to wrinkling. This is due to the presence of an aromatic ring within the monomers, which makes it quite strong/stiff; especially in this fibre form. These wrinkle-resistant fabrics are appropriately known as "permanent press fabrics."

To find out more information, I have included some sources below:


https://en.wikipedia.org/wiki/Polyester
https://en.wikipedia.org/wiki/Polyethylene_terephthalate
https://www.britannica.com/science/polyethylene-terephthalate