A stock option is just an option to buy a specific number of share of stock at a future date. A vesting option is basically a spin on that. Where the two get similar, though, is when a company is issuing the options to its employees.
A vesting option is when an employee gains rights to stocks provided by the employer over time. So, for example, an employer would earn 100 shares of stock today. They would then be vested, so he would gain access to the shares over time according to a set out schedule. Something like 20 shares after one year 20 more after the second year and then the remaining 60 after the third year. These are used for things like retirement funds and it allows the employer to give the employee an incentive to stay with the company. Further, the idea is that all 100 stocks will be issued to the employee at the current stock price as of when they were vested (in our example, the price as of today). So, the employee also has an incentive to work hard to raise the stock price over the next few years so that he can sell his shares, when he receives them, for a profit.
An employee stock option is basically the same as a vesting option. The only difference is that an employee stock option is just that, an option. It does not create an obligation on the behalf of the employee, he does not have to purchase the stocks in the future. [more on stock options here –]
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