Carry look ahead adder with 2-input gates?
Carry look-ahead allows a sum of any width to be computed in a fixed number of logic "levels" (layers of gates) between any input and any output. The downside is that it requires gates with as many inputs as there are bits in the numbers being added. Gates with high "fan-in" like that tend to be slower than gates with fewer inputs.

Any gate with a large number of inputs can be replaced by a group of gates that have fewer inputs. For example, an 8-input AND gate can be implemented as two 4-input gates feeding a 2-input gate.

Kogge-Stone, Brent–Kung, etc. are simply different ways of organizing the "trees" of logic that implement the look-ahead, using gates with a limited number of inputs. Picking a particular implementation depends on many things, such as the tradeoff between fan-in and speed for the technology being used, and on whether you put a higher priority on area or speed.