The determining factor(s) of how a disc performs is "pounds per disc" (over-all weight of disc, divided by number of blades) and disc spacing. With most offset disc's, they have the blades spaced 9" to 11" apart. Conventional disc harrows will usually be 7" to 9" spacings. All those things play into how deep they'll cut. In general, most offset discs will be set at a more aggressive angle too. Off set disc's are intended as a primary tillage tool. A disc harrow CAN be used for primary tillage in certain conditions, but usually with limited success. Generally speaking, a disc harrow with 7" spaced disc blades will be a "finishing disc", designed to leave a smooth, level seedbed.
Ground speed has a great deal to do with how a disc functions too. Too slow and you don't get the "soil action" it takes to break up clods. Too fast and they tend to want to ride up on top of the ground. Most modern day "AG" disc's work best around 5 to 6 mph.
You'll also find that uses for and terminoligy for a disc is a regional thing. In all my years, I've never heard anyone from my area refer to a disc as a "disc harrow". A disc is a disc, and a harrow is something you drag BEHIND a disc.
Most of todays "economy disc's" (If you can say that with todays prices) are a compromise at best. They're light enough for a small tractor to pick up. That hurts their overall performance, regardless of angle or disc spacing.
Often times you'll hear people recommend discing "multiple passes" to get to the desired depth. While that is true to some extent, remember that a disc also COMPACTS soil BELOW the depth it's cutting. (Just like a plow leaves a "plow pan" or compacted layer below its working depth) The more times you go over a field with a disc, the more you create a layer of compaction. That's why there are differet types of disc's. You want the job done in one or two trips over the field if at all possible. Beyond that you create as many issues as you correct.
Plows and disc's were the norm for decades of conventional farming. Nowdays the move is to no-till where conditions permit. Freeze/thaw cycles improve soil structure, doing naturally what farmers tried to accomplish with heavy, fuel guzzling equipment. In the areas where no till doesn't work as well, chisel plows, field cultivators, deep rippers, mulch tillers, disc rippers, and "zone builders" are rapidly pushing plows and disc's into extinction. Most new discs sold nowdays are for "hobbiests".