Ionian
Major.
This is the major scale. In the C example it runs from C to C. Sam uses it when the song is plainly major and the line should sound settled, like it already arrived home.
Greek modes
Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian
The scales Sam Castillo still uses when he plays guitar.
Where the names come from
Ancient Greek musicians and theorists worked these scales out from the tuning of strings and the intervals they heard. Pythagoras is the early figure in that line. The later harmoniai tradition carried the same kind of work forward. They tuned a string, listened to the interval it made, and wrote down the patterns that held together. It was tuning and listening, then writing. The modes were gathered that way over a long time.
They named the harmoniai after Greek regions and peoples: Dorian, Phrygian, Lydian, Mixolydian, and the others. Ionian, Aeolian, and Locrian belong to that same family of names. A harmonia was a tuning and a character of melody, tied to a place and a people.
The names on a guitar today come from that Greek tradition. Medieval church theorists reused the Greek names for a related system of chant modes. Related, with its own notes: those church modes, the old harmoniai, and the modern guitar modes do not match interval for interval. The names stayed in use. From here on, this page means the modern modes, which are the ones Sam plays.
On the guitar
Sam still uses these modes when he plays. He treats them as colors. Take the notes of C major, C D E F G A B, and start on a different note. Home moves, and the color moves with it. C is only the example. Slide the shape up the neck and the mode keeps its character.
He can also stay on one root and move the one or two notes that give the mode its sound. In a song, that is usually the faster way.
Dorian
Minor with a lift.
Minor, with the sixth left raised, so the line has some air in it. In the C example it starts on D. Sam uses it on a minor vamp that should still move, a groove that stays minor and does not turn heavy.
Phrygian
Dark.
The second is lowered, a fret from the root, and that closeness is the color. In the C example it starts on E. Sam uses it for a dark riff, or a Spanish sound, sitting on one chord.
Lydian
Bright, with a sharp 4.
Major, with the fourth raised. That one note opens the chord up. In the C example it starts on F. Sam uses it for a floating major line, when a plain major chord would feel too settled.
Mixolydian
Dominant.
Major with a lowered seventh, the note that makes a dominant seventh chord. In the C example it starts on G. Sam uses it for rock and blues, any major chord that wants to lean forward.
Aeolian
Natural minor.
The plain minor scale: flat three, flat six, flat seven. In the C example it starts on A. Sam uses it for a straight minor song, a ballad or a minor rock tune.
Locrian
Unstable.
The fifth is lowered, so the chord on the root is diminished and will not sit still. In the C example it starts on B. Sam uses it for a short tense pass, then he gets off it. He does not park a whole song there.