The OP got it wrong. He wrote "It was Non-B in 2010, then changed to Non RE when I got it transfered to a new passport. "
It is not the extension stamp that got transferred from the old passport to the new one. It was the arrival stamp put in the passport when he entered with a re-entry permit.
See the examples posted by Dr Jack54. NON-RE is not really correct; it should be just RE, as I have seen it on other arrival stamps of this type, unless immigration changed the practice.
This is one of those cases where it would have been useful if the OP had posted a photo of the stamp in question but I realise that doing so is not always easy.
Of course we cannot exclude the possibility that the latest arrival stamp in the old passport showed Non-B and this was corrected to NON-RE when it was copied over to the new passport.
More likely, though, since the OP wrote that it was Non-B in 2010, that arrival stamp was from the original arrival with a non-B visa 13 years ago, not the arrival stamp from his latest arrival in Thailand