The 1 TB Seagate Backup Plus hosts a 2,5 inch SATA disk internally, meaning the signal can be hooked up to a SATA-jack on your motherboard or an extrnal eSATA or eSATA/USB port, als known as eSATAp, instead of the casing interface. As a 2,5 inch drive, it can also receive power from the eSATAp port, even if this port does not support the optional 12 volt pins required to keep the phyiscally larger hard disks spinning.
Assuming SATA II, the interface would give you a maximum effective transfer rate of 2,4 Gb/s, as opposed to 0,28 Gb/s for USB 2.0 or 3,2 Gb/s for USB 3.0. These are theoretical limits. In practice, the HDD's throughput will not come close to maxing out these connections.
eSATAp cables that connect to the signal and power of 2,5 inch SATA drives are generally inexpensive. For the maximum transfer speed, you would have to open up the external drive's casing and connect the drive directly using a cable as in the image below. Though electronically compatible, keep in mind that SATA devices may not be designed to match the stricter eSATA requirements and may fail in hostile conditions.