It's probably the position.

Try activating your "core" muscles more to keep your weight on your sit-bones rather than letting the pelvis flop forward so the weight is on your soft tissue and pubic bone.

If that doesn't help (or if your posture is already good) you might need a different saddle for the road bike. (one that supports your sit bones better, or one that is more "T" shaped -for the chafing-, or one with less padding, or one with a deeper/wider/softer/more magical cut out, etc.)

You said you've always experienced discomfort biking. Is it possible you've always been on a saddle that isn't quite perfect?