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Yep, it's the same product, just the 'Training' name has been included with some products to allow other products into the range.
The fabric and features are all the same, but there was a slight adjustment to the sizing after the very first generation (it was on the tighter side, and following feedback was made more generous but this was years back) and a different country of origin.
I'm not sure. I've never used one but think it might be very similar apart from country of manufacture. @chopsicle is the best point of reference for product details.
If you have a serviceable PTJ then keep riding in that!