I'm a roadie that has been riding gravel now for about a year and a half in dusty and dry Southern California. I very rarely plan out my rides and go where the trail takes me, typically involving some asphalt connections, singletrack descents, stream crossings, fast hardpack, loose climbs for 15 to 40 miles. My first set of gravel tires were semi-knobby Continental SpeedRides in 700x42c. Very light and fast on hard pack and dug in well for loose climbing and cornering, but cost me a gear or two on the road. SpeedRides have ridiculously supple sidewalls, like they collapse when you change the tube. That meant that I banged the rims in rock gardens, which we have all over the place here, and suffered pinches every 3 or 4 rides. But man, those SpeeRides were comfortable and gave me supreme confidence on technical downhill.
When it came time to get new tires, a friend gave me some WTB Nanos in 700x43c which were extremely knobby. They made it through 2 rides before going up on eBay. They were heavy, slow, and loud and had a distinct "MTB" type of feel. I haven't owned a MTB in a decade. Perhaps that contributed to my dislike of the Nanos. If you are a MTB rider, then you might really enjoy this style of tire.
After researching Rene Herse's outstanding offerings and reading about what folks like Ted King and Lael Wilcox go for, I wanted to go with Herse's semi-slick Barlow Pass tires in standard or endurance casing. Unfortunately due to expenses on bikes that month, I couldn't make it work. It turns out that Panaracer and Rene Herse work together closely, so I opted for some Panaracer GravelKing TLC SS (semi-slick) in 700x38c for half the price. Panaracer is apparently the last company making bike tires in Japan (can anybody verify this?). The construction on these tires is beautiful. I have 8 hard rides on these tires. The sidewall casing is surprisingly sturdy and I have had no pinch flats yet. The tread is reminiscent of vintage touring tires from the 80s. They are almost as fast as my road tires on pavement, faster than anything on the hardpack, yet as comfortable as the SpeedRides overall. The only negative is that I have to keep my butt planted on the seat to maintain traction on the loosest climbs and corners. If you stand when you climb, these will slip on the loose dirt.
The cycling industry (manufacturers, magazines, reviewers) aggressively promotes knobby 700c tires, which certainly provide a more dramatic and badass look. Unless you are coming to gravel from the MTB world, it is my opinion that you will be ill-served by knobbies for all-around gravel riding. Hence the OP's question as to whether a true mixed use gravel tire exists is VERY interesting. After 18 months of gravel riding, I believe that a stout touring tire with a compliant sidewall at low PSI would be just fine in everything except mud -- if it existed in a 700x38c or larger. So perhaps gravel tires just mean a larger touring tire <grin>!