You said it the short (and clear) way. Thank you so much!

Anyway, here's the long explanation (since I already started writing it down):
You are right, but I'm talking about transposing instruments. When you have a piece of sheet music for an instrument, play what's written and the pitches that come from your instrument match the written stuff, that's a non-transposing instrument. By definition, that instrument is tuned to the key of C. Examples of non-transposing instruments are violin, flute, oboe, bassoon and piano.
But when the pitches that come out from your instrument don't match the printed music, you are playing a transposing instrument, and that means that it is not tuned to the key of C (which is considered the "center", "root" -or whatever you want to call it- key). So, in the same way the pitches are transposed from the actual ones, the key in which the instrument is tuned is also transposed.
So, what does it mean when you say that an instrument is in Eb (like an alto saxophone), in Bb (like a regular trumpet) or in F (like a French horn)? The best way to understand it is: All those instruments have a pitch which is called "C". But when you ask a French horn player to sound a "C", what you hear is an "F" if you play the same pitch on a piano. So, the note that's called "F" in "real life", it's a "C" for the French horn. Hence, it's in F. In the case of the alto sax, an Eb for the piano is a C for that instrument, so it's in Eb.
So, in the case of a guitar/bass, you know where to find a C note, right? Let's say the G string, 5th fret. That's the standard tuning for the instrument. But if you lower the whole instrument's standard tuning one half step, what you'll hear from the G string at the 5th fret is a B. Hence, the guitar/bass is not in C, but B. The basis for that assertion is the fact that, if you are presented with a piece of sheet music for bass and you see a C note, you automatically know where it's located. But oops! When you fret that C note in the place you've been taught, you don't hear a C but a B if the instrument is downtuned one half step.
BTW, guitar and bass are transposing instruments since the real pitches are different from those written for them. They sound one octave lower than written, so that makes them transposing instruments as well. But since the tuning difference is a full octave, it doesn't affect the instrument's key, which is still C.
Hope this helps.