Although the above post is true in regards to stock vs options, the difference between restricted stock and unrestricted stock is more simple.
Generally restricted stocks are subject to certain conditions, the most popular is a time commitment. Often they will give you a certain number of shares, and they will vest or become yours after 1/3/5 years, or a percentage per year. If you quit or are fired before the specified time, you don't get the unvested shares.
Just call your HR department and ask, they'll know.