You might be confusing the pitch of the instrument ( F in this case) with a key. No connection! (Otherwise horn players would only have to learn one scale!)
Because the horn is notated as a transposing instrument ( a relic from the days of crooks), it is referred to as being 'in' F. (nothing to do with any key, hang in with me here....)
Horn in F refers to the pitch of the harmonic series of the tubing, and by convention with horns the first, second and fourth harmonics are referred to as C by the horn player, when it is actually concert F. So if C on the horn is F on the piano, then a horn will always be notated in one sharp more than the piano.
Same notation convention applies for Bb trumpets, and their relatives in various pitches; the number of sharps different from concert pitch will vary according to the pitch of the trumpet.
DOESN'T apply for trombones (Bb and Eb) and tubas (Bb, C, Eb, F), we notate in concert pitch.