C major and A minor scales contain the same notes, but those notes take on different roles.
The root note is the "home" of the melody - often the melody begins or ends on the root note, but even when it doesn't, you should be able to hear how the melody feels "resolved" when it's on the root note.
C is the root note of C major. A is the root note of A minor.
The fifth is an important relative of the root, because it reliably harmonises with it - indeed if you listen carefully (on most instruments) you can hear the pitch of the fifth when you play the root note - it is a harmonic. It's called the fifth because it's four notes up the scale from the root (or first) -- but it's 7 semitones up.
G is the fifth of C. E is the fifth of A minor.
The third is really important because it's the difference between a major and a minor scale. If you play all the notes from a scale except for the third, you can't tell whether it's major or minor.
It's two notes up the scale from the first. But in a major key it's 4 semitones up, while in a minor key it's 3 semitones up.
E is the third of C. C is the third of A minor.
All the other notes have "roles" too (this isn't a formal music term -- I'm using ordinary language to explain things). You can study books to learn more, or just learn to feel the music.
So:
- in C, the 1-3-5 notes are C-E-G.
- in A the 1-3-5 notes are A-C-E.
You'll play A notes in C major melodies, but they will not take as significant a role in the structure of the melody. Likewise you'll play G notes in A minor melodies, but again they'll not be as "important" as a G is in C major melodies.
When soloing:
- As a rule of thumb, start and end on the root note (but rules are made to be broken!)
- Use the third to give a major or minor feel (or omit it to make it indeterminate)
On a piano, you could say that C major / A minor are the "most basic" keys, because the player can ignore black keys. In principle, though, every key is pretty much equivalent. C# major is simply C major with every note moved up one semitone.
There are easier keys than C/Am on a guitar, because more of the significant notes are open strings. However, if your intention is to solo, it's good to learn shapes that have no open strings. You can use these shapes in any key, simply by moving your whole hand up or down the fretboard.
