Sheet music is a type of printed music. The music that musicians have in front of them when they play is printed music.  The sheet or sheets of paper that contain(s) the written notation of what the musician are to play is called printed music.  Sheet music usually refers to a "single sheet" of music; that is, one song or piece printed separately.  Printed music includes sheet music but also includes music published in collections.  People often confuse sheet music with printed music.  

Sheet music can be published as a separate copy for one piece or song, or it can be a collection of pieces in a larger book. If there is a piece of music for violin and piano, then the pianist will play from the piano part, which will have the piano music written, as usual, on two staves.  Above those two staves, printed slightly smaller, will be another stave with the violin part.  The violinist will play from a separate part which will just have the violin music.  This means that the pianist can always see what the violin should be playing, but the violinist will not be able to see what the pianist is playing.  The violinist may need to look at the piano part sometimes to see how the violin and piano part fit together.  It would be difficult for the violinist to play from music with both parts because he would need to turn the pages too often.  (Unless the violinist had a few measures of rest right before the page turn, the violinist would miss playing some of his/her part while turning the page.)

Score

A  score  is printed music of a piece written for several instruments. The music (parts) for each instrument are written above one another on separate staves.  A conductor can see from the score what each instrument should be playing and how it fits together.  Each player only has his or her own part (the notes that that performer plays) in front of him/her.  From time to time, if the instrument has long period where he/she does not play (that is, has a block of rests), the publisher may print, usually in smaller type, a portion of the music another instruments (usually an instrument playing the melody) would be playing to help the performer know what to listen before he/she starts playing.  These smaller notes are called cues because it cues, or clues, the performer that he/she is going to start playing soon.)

Types 
 An orchestral score  or  full score  shows exactly what all the instruments of the orchestra play.  If the piece uses a large orchestra with many different instruments, the page must be very tall.  The conductor uses the score to be able to see which instruments are playing when.  The conductor would cue orchestra members (or sections within the orchestra) when they begin to play.  Conductors do much more than this (tempo, dynamics, interpretation, etc.), of course, but most conductors use a score when rehearsing the orchestra or when the orchestra is performing.
 A miniature score,  "study score," or  pocket score  is like an orchestral score but much smaller.  It will not be big enough for a conductor to conduct from because the print will be too small, but it will be good enough for studying, and it will be much cheaper than a large, orchestral score. 
 A vocal score  or  piano score  is the music for a piece for choir and singers (e.g. an opera) in which all the instrumental parts are printed on two staves so that it can be played on a piano.  Some notes will, of course, have to be left out to make it possible to play with just two hands.
 A short score  means a score where an orchestral piece has been written on three or four staves only.  It is something between a piano score and a full score.  A composer may write a piece in short score when composing it, and write out an orchestral score later.  Short scores are not usually published, they are just working copies while the piece is being composed.

Standard Score Order Format 
In an orchestral score, the order in which the instrumental lines are usually printed is:
 woodwind at the top (flute, oboe, clarinet, bassoon and any other special woodwind),
 brass (French horn, saxophone, trumpet, trombone, and low brass such as tuba),
 percussion (claves, tambourine, bass drum, xylophone, etc.),
 strings (violin, viola, cello and double bass),

If there is a choir or solo singers their part is written near the bottom, above the strings.  Except for vocal parts, bar lines will usually join up the staves of each family.  Not joining them for vocal parts allows greater flexibility for placement of lyrics.  Joining bar lines makes it easier to find the instruments than if they had been drawn all the way down the page. An experienced conductor knows score order well enough to examine a score and very quickly see which instrument plays a given part, even if the instrument names are not there. Below is an example of score order for a standard orchestral score as it would be listed alongside the staves.

Orchestral Format 

 Piccolo
 Flute
 Alto Flute*
 Oboe
 Cor Anglais*
Clarinet in Eb or A*
 Clarinet in Bb
 Bass Clarinet in Bb
 Alto Sax in Eb*
 Bassoon
 Contrabassoons
 Horn in F
 Trumpets in Bb
 Trombones
 Bass Trombone
 Euphonium*
 Tuba
 Timpani
 Other Percussion (Triangle, agogo bells, tam-tam glockenspiel, xylophone, vibraphone, tubular bells, tenor drum, bass drum)
 Other Instruments
 Harp
 Piano & Keyboards
 Choir (SATB)
 Violin 1
 Violin 2
 Viola
 Cello
 Bass

*Indicates a non standard instrument, these are instruments that are used because the composer wants the tone in the ensemble only

Concert Band Format 
In a band score, the instruments will be listed differently. Below is an example of score order for a standard band score as it would be listed alongside the staves.

 Flute
 Oboe
 Bassoon
 Clarinet in Bb
 Alto Clarinet*
 Bass Clarinet in Bb
 Alto Saxophone in Eb
 Tenor Saxophone in Bb
 Baritone Saxophone in Eb
 Trumpet in Bb
 Horn in F
 Trombone
 Bass Trombone*
 Baritone/Euphonium
 Tuba
 Pitched Percussion
Unpitched Percussion

*Indicates a non standard instrument, these are instruments that are used because the composer wants the tone in the ensemble only

Related pages 

Musical note
Musicology

References

Other websites 
International Music Score Library Project, a public-domain sheet music library with original scores scanned to PDF.

Music