(I'm not an economist either, but I'm also really interested in this)
> What's the difference in theory and practice between UBI and changing the standard deduction/marginal rate? Like if we give out $6k a year to everyone through a $500 check, what is the difference in how that money is spent versus if we increased the standard deduction to where people would pay $6k less in taxes? (assuming that people are in fact paying at least $6k)
You've partly answered your own question. One of the big differences is that people who wouldn't have paid at least $6k in taxes wouldn't get the full benefit. It's also true that the standard deduction is a deduction of your taxable income. Depending on your tax bracket, that's going to reduce the amount you owe by a different amount.
We could instead talk about doing it as a tax credit similar to the Earned Income Tax Credit, but giving it to everyone equally regardless of whether they're working. This would be more like a basic income. If we can pay people the tax credit at finer intervals instead of in one lump sum at the end of the year, that's even better.
The disadvantage is that people would still have to file tax returns. The people who need the money the most are also the ones who are least likely to be able to navigate the system. If it's exactly the same amount of money to everyone unconditionally, then we reduce the bureaucratic burden by not tying it to the tax system.
Here's a video where I answer the question of why basic income should go to rich people. I advocate keeping the complexity separate from the cash benefit system and putting all that complexity on the taxation side.
https://youtu.be/ylm1jN9cMRQ?t=430