This is different. Edit; Seems like a marketing ploy to expand shelf presence and appeal to a wider audience(?).
All four variants are on Amazon and you can view the ingredients and order of ingredients. See below ...
I don't recall wheat being in Za'atar.
I used to get Za'atar sent to me from a friend (sometimes they were in Lebanon, sometimes in Jordan) and they didn't vary. The "thyme" wasn't typical thyme, it was wild thyme grown in the region (may also be called hyssop). They have moved on in their travels, but I can still get "very close" Za'atar from Salloum Bros on Amazon (https://www.amazon.com/Lebanon-Zaatar-Lb-Salloum-Bros/dp/B0199B09ME).
I found a link about Hyssop and Za'atar - https://thespiceway.com/pages/the-truth-about-zaatar. there are other sources.
Links to pictures of ingredients in OP's Za'atar brand/variants: