Like Cheeko Marx once said "If you look at it, it's a barn, if you smell it, it's a stable" I think the terms are interchangeable
Here is what Wikipedia has to say: "A gold bar, also called a gold ingot or gold bullion, is a quantity of refined metallic gold of any shape that is made by a bar producer meeting standard conditions of manufacture, labeling, and record keeping."
An ingot is a piece of metal that will most likely be used for turning into something else such as jewelry or coins...The shape doesn't really matter, it can be a ball, cube, or any other shape.....I wouldn't call a 10 ounce PAMP Lady Fortune bar an ingot because I feel that the silver is in it's final form for decades or centuries but I would call a 10 ounce bar of the same purity and shape but without the art and the big name mint stamp an ingot because it has a much higher chance of being turned into something else in the near future. If it's in it's final form it's not an ingot.
An ingot can be of any shape, so a bar is a catagory of ingot. An ingot does not have to be metal btw. There are some crystal and silicon ignots for example that were heated then cooled in a controlled manner that does put them into what one would call a final form. Kind of like you can not turn glass back into sand, but PM's can be melted and recast as you are purifying the material.
Crystal and silicon ingots are used for things such as the fabrication of semiconductor devices.....Ingots are not intended to be in final form.
I think this comes down then to a persons understanding of final form. In my undersanding, the crystal/silicon ingot is in itself in final form. It will be added to a device thus putting the device in its final dedicated form. Coins for example can be added to a holder, does that change that the coin is considered to be in it's final form?