It's all about where your money is coming from, and where you're sending it.
A 60-day rollover is the process of moving your retirement savings from a qualified plan, typically a 401(k), into an IRA. The funds are distributed to you and must be re-deposited within 60 days to avoid tax penalties. You initiate the rollover request and are limited to one rollover per year, per account.
A direct rollover occurs when your account assets are transferred directly from one IRA custodian to another. Transfer requests are initiated by your new custodian. There are no tax consequences to a transfer and no limitations on the number of transfers you can make.