SATA I (revision 1.x) interface, formally known as SATA 1.5Gb/s, is the first generation SATA interface running at 1.5 Gb/s. The bandwidth throughput, which is supported by the interface, is up to 150MB/s.
SATA II (revision 2.x) interface, formally known as SATA 3Gb/s, is a second generation SATA interface running at 3.0 Gb/s. The bandwidth throughput, which is supported by the interface, is up to 300MB/s.
SATA III (revision 3.x) interface, formally known as SATA 6Gb/s, is a third generation SATA interface running at 6.0Gb/s. The bandwidth throughput, which is supported by the interface, is up to 600MB/s. This interface is backwards compatible with SATA 3 Gb/s interface.
SATA II specifications provide backward compatibility to function on SATA I ports. SATA III specifications provide backward compatibility to function on SATA I and SATA II ports. However, the maximum speed of the drive will be slower due to the lower speed limitations of the port.
Example: SanDisk Extreme SSD, which supports SATA 6Gb/s interface and when connected to SATA 6Gb/s port, can reach up to 550/520MB/s sequential read and sequential write speed rates respectively. However, when the drive is connected to SATA 3 Gb/s port, it can reach up to 285/275MB/s sequential read and sequential write speed rates respectively.
https://kb.sandisk.com/app/answers/detail/a_id/8142/~/difference-between-sata-i%2C-sata-ii-and-sata-iii
You can use a SATA III 6Gb/s SSD on a motherboard supporting SATA 1.5Gb/s or 3Gb/s interface. However, the transfer speed will not reach the defined level of SATA 6Gb/s.
What does 6gb/s mean?
SATA III (revision 3. x) interface, formally known as SATA 6Gb/s, is a third generation SATA interface running at 6.0Gb/s. The bandwidth throughput, which is supported by the interface, is up to 600MB/s. This interface is backwards compatible with SATA 3 Gb/s interface.
What is SATA 6g?
SATA 6G - Computer Definition
The SATA 3.0 (SATA III) hardware interface with a 6 Gbps data rate. See SATA