A tax write off is also called a tax deduction.

So when you do your taxes and you need to pick between the standard deduction or itemized, that’s picking if you want to write off the standard amount or try to find all the amounts that might apply to you.

The deductions, or write offs, reduce your income for tax purposes. So if you have 50k in taxable income, a 10k deduction will mean you’re only taxed on 40k.

To get something you would call a discount, you would need a tax credit, which reduces the bill by some fixed amount.

10k write off: 100k income becomes 90k, 20% taxes are 18k.
10k credit: 100k income at 20% is 20k, less 10k credit is 10k is taxes.

Movie studios do complicated accounting to make it so the business that collects the money for showing the movie is often not the one that made the movie.
That means that often the movie is able to be described as a financial failure even though it made more money than it cost to produce.
Usually this isn’t done for tax purposes, because the IRS will generally get their cut regardless, since if the movie makes money, someone is collecting it.

Entertainment often pays actors, writers and such royalties based on a proportion of profits. By manipulating which specific entity actually shows the profit, they can manipulate how much royalties they have to pay.