Yes, tickets won't be any different, except for who to talk to In case you need to make a change. Other differences might be change or cancel fees, restrictions (can they be changed/canceled at all), definitely fare class and that potentially affects whether you can earn mileage on a partner program or not. Your tickets on the Thai site likely must be issued in Thailand.

From my experience in looking at Thai tickets, a couple of domestic though mostly India-Thailand, Thai has a lot of country-based restrictions on their discount fares. In the instances I've looked at, they will only sell pretty much Y fares through US-based OTAs. In my cases in booking India-Thailand, going through an India-based OTA or Thai airlines website directly, which switches to country-based site based on origin, and allows discount fares to be booked, in many cases - the fare on booking ex-US sites were pretty much double of what I could find from getting tickets issued in India.

So your experience pretty much mimics mine.