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I know that a french horn in F means, that instead of playing a C it plays an F, and the same with E flat.

But why are there french horns in F AND french horns in E flat? Wouldn't the only difference be the notation?

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This is a vestige of the history of the horn. Before the Industrial Revolution, the only horns that were available were natural horns. Natural horns can't play a full chromatic series; they sound best on the notes of a harmonic series whose base note is determined by the physical length of tubing in the horn. It is possible for a skilled natural horn player, through various tricks, to play nearby notes as well, but they still don't have the full chromatic range (particularly in the lower range of the instrument where the notes of the harmonic series are widely spaced.) So a natural horn would have a "natural key" in which it sounded best.

To get a bit more versatility, horns used crooks to change the keys they were pitched in. These were interchangeable lengths of tubing that the player could swap out on the instrument, allowing them to change between harmonic series in the middle of a piece. Effectively, this allowed them to modulate with the rest of the orchestra, going from being pitched "in F" to being pitched "in E-flat". This swap couldn't happen instantly, but it was better than sitting around with nothing to do for an entire section of a piece.

Around the start of the 19th century, technology advanced to the point where piston and rotary valves could be made to the tolerances necessary to be used in brass instruments, and the valve horn as we know it (along with the valve trumpet) was born. Berlioz's Treatise on Instrumentation (1845) is illustrative of this development; he devotes long sections to both the use of the natural horn and the new-fangled valve & cylinder horns.

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