Carbide
When tool-makers refer to "carbide" they're really referring to a special alloy containing carbide. There are several kinds of carbide compounds. Carbide used in tools is tungsten carbide. Tungsten is among the hardest natural elements. Cobalt is also used -- another of the hardest natural elements. These materials are milled by superheating them, resulting in tool-grade carbide.
Core vs. Tip
Carbide cores should not be confused with special drill bit tips. For example, some drill bits are made with ultra-hard tips, possibly made from cobalt. The entire bit doesn't need to be ultra-hard; just the cutting edge which is attached to a steel shaft. Carbide cores use a design with a central cutter and an out cutter, like a hole saw.
Hole Saw Design
Carbide core drill tips can be described as hole saws for concrete, rock or steel. You may have seen a hole saw used to cut the circle out of a door to accept the door knob. Wood hole saws use a cup-shaped piece of metal with teeth ground into their lip. Through the center of the cup or cylindrical saw is a standard, wood twist bit. The twist bit penetrates first, centering the hole, then the outer blades cut a cylindrical channel which is easier to remove because of the pilot hole. Carbide cores cut the same designs even though their central bit uses the ultra-hard carbide alloy either as a tip or completely through the bit.
Outer Teeth
The outer cutting teeth on carbide core drill tips are specially designed for harder materials like concrete. They may also used carbide-tipped cutting edges, industrial diamond or other industrial cutting materials. These outer teeth are likely inserted like fine circular saw blades, rather than the old filed-and-bent sawtooth designs found on hole saws.