The CY2309SXC-1 is the base part, while the CY2309SXC-1H is the high-drive version of the -1. The -1H devices operate at up to 100-/133-MHz frequencies, and have higher drive than the -1 devices. This information can be found in the Functional Description section of the CY2309 datasheet.
"High-drive" means the output buffer supplies more current than standard drive. This results in faster rise and fall times, which may be important if timing is critical in the application. Higher drive outputs can also drive larger loads better (again, with faster rise/fall times compared to standard drive).
Both high and standard drive have the same frequency specification.