I saw something at the grocery store that was labeled post-biotics. What is the difference between all these things? Are any of them really helpful?
My understanding agrees with Google AI, " Prebiotics (fuel), Probiotics (live bacteria), and Postbiotics (waste byproducts) work together in a continuum to support gut health, immunity, and digestion. Prebiotics feed probiotics, which in turn produce postbiotics, creating a balanced microbiome that helps reduce bloating, improve nutrient absorption, and strengthen the immune system."
I’ve heard of pro-biotics, which are supposed to promote a healthy biome in your digestive system.
But pre-biotics or post-biotics? Sounds like marketing woo-woo to me. I’ll want to see some properly controlled scientific studies before I take it in any way seriously.
That’s the bar for declaring something more than marketing woo? Sheesh.
Is “Designed to support…” a term that means anything medically and/or legally?
Oh the evidence on prebiotics is vast, but generally a decent diet provides them (and is in my opinion much preferable): think fiber, resistant starches, and poorly digested oligosacharrides.
Probiotics too. Probably best by way of fermented foods with active cultures. In addition to the bugs you get the products of fermentation that may do some good stuff too.
Postbiotics? Less solid evidence but non-zero. Just close to zero! 
And nothing that shows an advantage or added benefit over having say a cup of yogurt with some chia and/or flax seeds and berries.
Theoretically if someone is immunocompromised I guess?
A minimum bar. Argument from authority, and all that.