"STYLE" is a Yamaha term for its Auto-accompaniment modules. "RHYTHM" is a Casio term for its Auto-accompaniment modules.
If you are talking about the PSR-3000 factory installed pre-set styles, you can just download them from the PSRTutorial.com library onto a USB flash drive and use them directly from that on the PSR-S775. If you are talking about User styles that are stored in internal memory, just save them to a flash drive and port it to the S775. If you are talking about User styles that are already on a flash drive, just unplug it from the PSR-3000 and plug it into the S775. They will work from the flash drive on the S775 the same way they did from the flash drive on the PSR-3000.
In every case though, you may need to do a considerable amount a voice (sound) tweaking to get them to sound correctly on the S775. There are considerable differences between the the 3000's voice set and the S775's voice set. The PSR-3000 was released in 2004, so its voice set is 16 years old.