A jointer brings adjacent sides to a square corner, while flattening the side on the table. But you can still end up with a piece that is not parallel in width and/or thickness.

A thickness sander doesn't square corners, but rather brings two opposite sides parallel with each other, as it flattens the side against the drum.

I have both and they see about the same amount of use.

I made a bunch of backed bows before I had the thickness sander, but wouldn't give it up now for anything. Back when, I would cut slats out of staves by using the bandsaw and table saw. Before that, I did a few by flattening staves with a Makita power hand planer, then prep the gluing surface with a toothing plane... but it was torturous in comparison.

Aren't thickness sanders and lam grinders essentially the same? In as far of how they work and what they do?

Yes.

I think you could make a decent lam grinder without breaking the bank ...

Yeah, I'm going to make my own lam grinder this weekend. I'm going to look for a good, used belt sander. Or, if that doesn't work, my local Harbor Frieght is going to have there belt sanders on sale for $60.