If the stock is $100 when it vests, you pay income tax on $100 per share, whether you hold or sell. It's exactly the same as if you got paid that money in cash and then decided to buy shares (after paying tax).
If you then hold and it goes above $100 while you held, you pay capital gains tax (short or long-term, depending on how long you hold) when you sell.
Again, exactly the same as would happen if you bought those shares yourself with a cash bonus. Getting shares really is the same as cash, for tax purposes.
I still don't get how there's any way holding it instead of selling it reduces taxes.
If you sell on vest, you pay income tax and 0 capital gains. If you sell after vest, you pay the same amount of income tax, and possibly nonzero capital gains.
Well... if it's worth $X when it vests, you pay income tax on $X. If it's worth $Y when you sell, you pay capital gains on $(Y - X), presuming you held it longer than a year. If it was less than a year, you pay income tax on $(Y - X).
At least, that's my understanding. I'm not a tax accountant, though. This is not financial advice.
There is no clarification to be made. There is no way to reduce taxes on RSUs by holding onto them longer. When $100 of RSUs vest, you get taxed on $100 of income. You can either keep the stock or immediately sell it with no further tax event related to that initial $100 whichever of the two options you choose. If you keep the stock, it is equivalent to having bought $100 of stock at that instant. Psychology aside, the hold versus sell-on-vest decision should be predicated entirely on whether you would have bought that amount of stock with your own cash at its vest price.
But you don't have to hold $company stock to do that. You can sell on vest for 0 capital gains, then buy diversified index funds and hold those long term.