Coda is the concluding passage of a piece or movement, typically forming an addition to the basic structure.
D.C. al fine is an indication to repeat from the beginning of the music, and continue until you reach the final barline or a double-barline marked with the word fine.
In music notation, dal segno, often abbreviated as D.S., is used as a navigation marker. From Italian for "from the sign", D.S. appears in sheet music and instructs a musician to repeat a passage starting from the sign shown at right.
Da Capo al Coda (often abbreviated as D.C. al Coda): Repeat from beginning to an indicated place and then play the tail part (the "Coda"). It directs the musician to go back and repeat the music from the beginning ("Capo"), and to continue playing until one reaches the first coda symbol.
D.S. al fine means to start back at the segno mark and continue playing until you reach the final barline, or a double-barline marked with the word fine. This command stands for dal segno al fine, and literally means "[play] from the sign to the end."
