landscape

Any difference in shooting in the landscape picture style or in the landscape basic zone mode?

Two entirely different settings. Picture style is dealing with processing settings such as contrast, sharpness, and saturation. The zone mode settings are dealing with camera settings such as shutter speed and aperture. I'm sure this is all explained quite clearly in your manual.

If you shoot raw you can ignore the picture style because that is just used to convert the Raw to jpg, so you can pick the settings you prefer when process the raw.