OK, I get the "diagonal" thing, it's a good name for it actually...
...consider that there are 2 components to playing different pitches on the strings of a Bass guitar:
1) Playing different strings (E-A-D-G, ascending in pitch)
2) Fretting (a particular string) at differnt frets (each fret "up" the fingerboard results in a different pitch; for example --> on the E-string, starting from an open E, moving up fret-by-fret, we have E-F-F#-G-G#-A-A#-B-C-C#, etc..)
...I guess you could call the 1st component the "Horizontal" component (altering pitches by plucking different strings)
..and then you could call the 2nd component the "Vertical" component (the "vertical" direction being from the open string up through the frets, 1st fret, 2nd fret, 3rd fret....---> Xth fret, depending on how many frets your fingerboard has)
Now, you COULD play any scale VERTICALLY ONLY, just playing one string and fretting appropriately.... but it's a hinderence, coz one you'd have to change L.H. positions every 4 notes....RATHER than do that, we have a higher-pitched string to switch to; if we were starting out on the E-string, we could continue on the A-string, thereby avoiding a shift in Left-Hand position...
...so in the case of playing, say, a 2 octave scale - we can't reach all the notes within a single L.H. position (I'm assuming 4 strings here), so we need to play at least the higher parts of the (2-octave) scale in a differnt position to the lower parts...
...You'd still utilize all strings, but your L.H. would ALSO move "up" the neck (towards the higher frets) to have access to all the notes....
===> and THAT would be called playing a scale "diagonally"
..
