The difference between the two are that your brokerage is required to report the cost basis of covered shares to both you and the IRS. Your brokerage isn't required to report the cost basis of noncovered shares to the IRS, only to the taxpayer.
For noncovered shares, you will have to enter the cost basis (what you paid for it). If you don't know it, you will have to enter 0, which means that you will pay more taxes on the sale of the security.
If you need help finding the cost basis, refer to the TurboTax article How do I find a stock's cost basis?