my friend who plays alto sax showed me his chord chart, in relation to tenor sax it was a step down
That can't be right.
Another way to view this is that when a player of a transposing instrument looks at a written "C" and plays what they call a "C" note they make the sound of the name of their instrument. In Other Words: When a Bb trumpet player sees a "C" and fingers a "C" the SOUND of the note is Bb. Alto saxphones are in Eb so when they see a "C" the sound is an Eb. French horns are in F... so they will sound an F when they are playing they note they call "C".
The term 'Concert' refers to the pitchs that a piano would play. Bass is in concert pitch (although we sound an octave lower than the written pitch). So are all the string instruments. Flutes and oboes are in concert pitch. Most wind instruments are transposing instruments of some kind. Except for tuba, all instruments that ready bass clef are concert pitch.
All of these instruments can play in any key, but they have to make adjustments so that their sounds will match the concert pitch. If you call "Bb Blues", the bass, piano and guitar will play in the key of Bb. The trumpet will play in their key of C and the Alto sax will play in their key of G.... and all will be good together.
This can be confusing (obviously) the first time you encounter transposing instruments, but its not really rocket science, just something you have to get in your head if you are going to write music for these instrument. FWIW, it is generally expected of professional players to be able to tranpose (at sight) concert pitch charts for their instruments. But, if you are on the studio clock, it pays to transpose the charts for them.