The technique is much different. I use a touch of pressure with the straight but none with my safety razors. That's because the DE blades are sharper overall than straight blades (and I'm making my comparison based on a straight that was made shave-ready by someone with experience).

Pressure makes the DE blade shave skin. That leads to irritation, razor burn, etc. No pressure at all will give you an amazing shave. Let the weight of razor do the work. I set my Gillette adjustables to 9 and beyond, which creates blade exposure that requires me to fully support the weight of the razor and use careful touches to remove my beard. The shaves are top notch, but attention to technique is critical.