If it becomes a part of the product that goes out the door (including the actual going out the door) you don't pay tax on it but you are responsible
for collecting tax on it or verifying that a valid sellers permit is held so that tax is eventually collected on it.
In our industry this pretty much only means garments, inks (including foil and any post-press stuff) and shipping. Nothing else.
If you purchase something tax free out of state and use it in your business you are expected to pay tax
on it as well.
Use tax means you bought something tax free but ended up using it for a taxable purpose, IE wearing a wholesale shirt yourself.
(which harkens back to my question a few weeks ago, if you scrap a shirt but an employee ends up wearing it?)
I would be very suspicious of anyone that told me I didn't have to pay taxes on a piece of equipment used in manufacturing.
I would also point out that at least in CA much of the responsibility for verifying/collecting that tax falls on the seller.
It's really not that complicated. Pay them now or pay them (more) later.