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 notes 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 leader 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.