Stick options and RSUs

I typically get an end of the year cash bonus. This time in addition to the cash bonus, I was offered some stock options at a certain price and also some RSUs. There is a vesting protocol for both.

I did some research into this and found out that for the stock options, once they vest I need to buy them at the predetermined price. While for the RSUs, they basically have the same value as a regular stock and I do not need to buy them. The RSUs are just given to me and when they vest, I can keep them or sell them.

Now my confusion is about taxes. For the stock options, when I buy them, what happens if the price of the stock is higher than the price at which I buy them? Do I need to pay any taxes on the difference? Also, what if I buy them and then sell them right away? Will I pay long term or short term taxes on the gains. If it helps, the partial vesting starts after the first year from the grant date.

For the RSUs, I can either hold on to them or just sell them. How would taxes work in either case?

I appreciate any insight on this as this is the first time I am dealing with these