When Timothy Cook was named CEO of Apple in August 2011, he got more than just a promotion: He was awarded 1 million shares of Apple stock, valued at $376 million. And a few months later, the company decided to raise his base pay from $900,000 to $1.4 million. All told, Cook’s 2011 compensation package was valued at $378 million, according to documents filed with the Securities Exchange Commission last week.

Commentators were quick to draw a contrast between Cook’s pay package and that of his predecessor, the late Steve Jobs, who famously received compensation of just $1 per year. But executive compensation – at Apple or any other large, public company – is a lot more complex than these numbers might suggest.

Let’s start with Jobs.

He did, indeed, receive just $1 in annual compensation from Apple, according to SEC filings. He received neither bonuses nor stock nor 401(k) contributions from the company. Jobs’ other major corporate role, as a member of the board of directors at Disney, was also uncompensated, per his request. But that does not mean he did not profit from his efforts to improve the two companies’ performance.

Jobs was the largest individual shareholder in both companies. He held 5.5 million shares in Apple; only investment firms BlackRock and Fidelity owned more. Jobs also owned 138 million shares in Disney – 7.1 percent of the company’s stock. Thus, his compensation was tied to the fate of the companies. In the five years before Jobs’ death, Apple stock rose from $75 per share to $378 per share, increasing the value of his stake by nearly $1.7 billion.

“While Jobs served as CEO, the company believed his level of stock ownership significantly aligned his interests with shareholders’ interests,” the latest Apple SEC filing says.

Cook’s compensation is structured somewhat differently. The stock Cook received upon his promotion was intended to reward the new CEO for staying on-board long-term. The value of the shares counts as part of his 2011 compensation for federal reporting purposes, but his shares are not yet vested – that is, he does not yet fully own them, nor can he sell them. Half of the stock will vest in 2016, if Cook is still with the company. But he has to stick around until 2021 to receive the remaining 500,000 shares. Cook will also continue to participate in the executive bonus program and stands to bring in as much as $2.8 million if the company has an especially strong performance this year (he received a bonus of $900,000 in 2011). In the category of "other compensation," which is where benefits and perks such as air travel and insurance coverage are reported, Cook received $14,700 in contributions to his 401(k) plan and the payment of $1,820 in life insurance premiums.

So how do Jobs’ and Cook’s pay packages compare to those of other prominent CEOs?

At Apple’s traditional archrival, Microsoft, CEO Steve Ballmer earned $682,500 in 2011, and an equal amount as a bonus, according to SEC filings. Ballmer also owns 333 million shares of Microsoft, worth about $9.4 billion as of January 2012. Robert Iger, President and CEO of Disney, received total compensation of $29.6 million in fiscal 2010, the last year for which the SEC report is available. This total includes $2 million in salary, $11.7 million in stock and stock option awards, a $13.5 million bonus, $192,000 for personal and business air travel, and $562,000 for security.

Amazon.com CEO Jeffrey Bezos receives an annual salary of $81,840, according to the company’s SEC filings. He also owns more than 88 million shares of the company's stock – almost 20 percent of the outstanding shares – a stake that was worth about $15.7 billion as of last week. Bezos’ total compensation package also includes $1.6 million in spending on personal security.