The 50% on receipt number comes from your marginal federal tax bracket plus state -- same as if the dollar value were additional gross (pre-tax) income.
The 20% on growth number (potentially 25-30% including state) is what you'd pay on capital gains -- same as if you'd taken this extra income as cash and invested it in anything.
Also one quirk of microsoft is since they have a half-title promotion system, as I understand it, it's normal to get refreshers on years 1-3 through a 4 year vest after a half-title/one-level promotion.
Usually you’re given a number of shares when you join, and the value of those shares change as they vest. This can lead to some really overinflated comp packages if a person joins before huge growth that a new person would not get.
There’s often restrictions around when you can sell while still employ by that company to avoid insider trading laws, like you can sell right before earnings reports.
For public companies, the vest date is also the release date, which is when the shares are recognized as income. You have to pay taxes when they are released, which is basically 25% federal tax plus whatever your state's tax rate is for this (10% in CA). To pay the taxes you can either deposit cash to cover the amount and keep the shares, or sell some fraction of the shares on the release date.
If you keep the shares, then any gain after the release date is taxed as capital gains. Basically, from a tax perspective it's equivalent to the company paying you cash on the release date equal to the stock price of your shares and you buying shares with it.
There are other options than purchasing the options yourself or just letting them expire.
From a pure finance perspective, you just need to find someone to take on the risk of the exercise. My company, ESO Fund, has a diversified portfolio of startups and as a result can take a $20k bet with much more ease than a single employee making a $20k bet.
I worked at a small series B level startup, and when I left I had the option to buy my shares at the last valuation price, but at just over $20,000 total I declined. I decided I could use that capital better than waiting around hoping they explode and get acquired. I don't think stock options work the same with public companies though.