Yes and no. Like gasoline, there are a handful of companies who supply the oil and maybe refine it. There are differences between them though. Probably in the additives and the quantity of each.
One of them has a reputation for sludging, I think Quaker State and it may only be their base dino oil product.
Most of the cheap synthetics tend to be super refined dino oil and the better brands, true synthetics that are made from natural gas and other products.
In any case, most come from a handful of suppliers. I believe most of it shares the same tankers and pipelines for transport. So, it does beg the question on if they are really different. Even the ones that supposedly come from Texas or Pennsylvania. Supposedly Quaker State and Pennzoil come from PA stock. But then there is the pipeline, tanker, and refinery thing.