It really is only in recent years that the "terminology" has become confusing, as back in the 1970's and 1980's, the only thing we used ortho/litho film for, was making high contrast images, such as line art for title slides, masks for background dropouts, and "high contrast conversions" of continuous tone originals for graphic design effects. I always used Kodalith A & B developer, which was a very active BLACK AND PURE WHITE DEVELOPER.
Now that "Lith" means a type of printing technique with specific developers and papers, the classic understanding of these thin emulsion ortho sensitive films is misunderstood, I think.
In general (with few exceptions) an "Ortho" film as available today is a thin emulsion (not necessarily thin base) orthochromatic sensitive film designed for high-contrast work, using specific developers designed to enhance this effect.
HOWEVER, you CAN get full toned results from these same films by developing them in soft-working (as compared to normal for these films) developers. Most b/w film developers for common films would be considered "soft working" in the context of using them for Ortho film.