Short version -- Ranch Rifles have integral scope mounts while the older Mini-14 doesn't. They can also be chambered in 7.62 x 39 (Mini-30's are often Ranch Rifles), while a Mini-14 is chambered in .223. I think you could basically (but maybe too simplistically) say that all Ranch Rifles are Mini-14's, but not all Mini-14's are Ranch Rifles.
Long version -- There are other differences based on when the rifle was produced. An older Mini-14 will have a single blade front sight, no scope mounts and a thin barrel profile. Older Ranch Rifles will have the single blade front sight, a thin barrel profile and integral scope mounts. Some newer Ranch Rifles have protected front sights, integral sights and thin barrels. The most recent rifles (both Ranch and Tactical) have integral scope mounts, protected front sights, a thicker/tapered barrel profile and maybe a flash hider on some models. I'm sure others can chime in more specifically with how the serial numbers correlate to production changes. I have a 183-series Mini-14 that has no scope mounts, single front blade and thin barrel, and it's marked Mini-14. I also had a 197-series Mini-30 that had the scope mounts, single blade sight and thin barrel, so it was marked Ranch Rifle. I believe the protected front blade sights started being typical with the 580-series about five years ago. I don't know at what serial number the thicker, tapered barrels became typical, but I know it's only been in the last couple years.