Originally Posted by: equatorThe Diatonic Scale evolved from two Tetrachords [C-D-E-F] and [G-A-B-C].
From those two Tetrachords you get the seven notes which correspond to the white keys on the piano; consisting of five tones and two semitones with no accidentals.
The Major and Minor Scales or the Church Modes with no sharps or flats are Diatonic.

Accidentals are notes that are outside the key in which a piece is written.
For example in the piece Fur Elise, the key signature is A minor, but the very second note is an accidental(D#) because it is out of the key signature.
Another example is the piece Fugue in G minor.
The key signature features Bb and Eb, but several times in the piece J.S. Bach places E natural as accidental because it is out of the key signature.
And it is not necessarily chromatic because the note before that is sometimes a fifth lower.

If a note is played outside of the key it is chromatic. It doesn't matter how many steps above or below something is. If it's out of key, it's chromatic. Furthermore, how can Fur Elise be in A Minor if the starting note is E? Anyway, that would still be chromatic.

An accidental is the symbol used to show when a note is sharp, flat, or natural. I've posted links to sources confirming everything that I've said on this so far.