The Natural Horn is the ancestor of the modern-day Valve horn.
It has no valves and less, or no tuning slides and is therefore a very conical tube.
A trombone & trumpet are more of a cylinder with a bell at the end, where Cornet & horn are gradually bigger throughout.
The natural horn has crooks to change its overall length, but is basically a tube that works as a single vibrating column. A single string of a violin can be cut in half to make an octave jump or 1/3 to make the fifth etc. Like that, the horn has the same overtone series. 15+ basic tones that can be altered by the hand in the bell or the chops to play equal tempered scales, melodies etc.
It wasn’t until the 1830’s that composers really started to write for valve horn. The most prominent was Schumann who still wrote for both natural & valve horn together. The use of this instrument is coming back with the authentic practice or historically correct performances.