There are many types of written music including traditional (classical) notation, jazz big band or combo charts, and pop music charts. I would like to describe the different kinds of notation and their advantages and disadvantages. This can help you know what kind of chart would be the best for what you are trying to accomplish.
Types of Written Music (see below for examples)
Traditional Written Music (Classical)
Jazz Charts
Pop Music Charts:
Piano/Vocal/Guitar (PVG)
Chords and Lyrics Chart
Chord Names Chart
Number Chart
Traditional Written Music (Classical)
This style of notation is probably the oldest, can be the hardest to read, and also contains the most information. For this you must know the different clefs and how to read them on your instrument as well as rhythmic, dynamic, and tone symbols (often shown in Italian). It also includes detailed descriptions of phrasing, articulation, and tempo. While this doesn’t leave a lot of room for interpretation it absolutely gives you all the information you need to recreate that piece of music. Classical music gives each instrument only their own written part however the conductor reads the Score, which contains all the parts together. One exception to this would be choral music, which shows all the parts so the singers can see the intervals between themselves and the other voices. On a smaller scale, this can be great for writing out a specific part for any instrument in any situation, although you would have to be aware of what clef the instrument uses and whether or not it is a transposed instrument. It would be difficult to transpose traditional notation to another key without the use of software.
Page 1 of the Score for "Symphony No. 5" by Ludwig van Beethoven (Traditional Written Music):
Jazz Charts
Jazz notation contains a lot of information but is also difficult to read because of the many possibilities of notation types within one chart. A Jazz Chart will commonly switch from traditional written music to showing chord names with rhythmic notation or simply slashes for comping, requiring the player to choose their own rhythms. There is also the chance of having a solo section where the musician is expected to improvise something over the chord names shown. Jazz Charts can be written out as a Score and individual parts for each instrument or the song can be combined into a “Lead Sheet” so that all players are reading the same thing. Even Jazz Lead Sheets will have a lot of information for the band including any important hits or figures. Jazz Charts cannot easily be transposed (unless you have an app) although jazz players will sometimes be asked to transpose in their heads, especially horn players who end up having to read a chart in concert key.
Lead Sheet for "Beauty and the Beast" by Wayne Shorter (Jazz Chart):
Piano/Vocal/Guitar (PVG)
This type of pop music chart is commonly found in publications like transcription books of famous music. PVG is nice for the pianist and vocalist because their parts are completely written out so that they can easily play the song note-for-note (it should be mentioned however that the written piano part is often a reduction of a group of instruments). For other instruments it is not so good unless the musicians can glean harmonic rhythm and figure information from looking at the piano part. Guitar chord names are shown above the staves sometimes with diagrams as well which is useful as long as they are good voicings (guitar chords can be tricky to voice and the people who make these books don’t always know what they’re doing with guitar). No information on strumming or picking patterns is given and unfortunately there is nothing else for the rest of the band. This style also has the disadvantage of not being easily transposable to other keys or instruments.
Page 1 of "Wait" by Sarah McLachlan (Piano/Vocal/Guitar):
Chords and Lyrics Chart
Mainly found online, Chords and Lyrics Charts have just that: the lyrics typed out with chord names placed (hopefully) directly above the word or syllable with which they occur. These are great for vocalists or vocalists accompanying themselves while not so great for instrumentalists because of the lack of specific information about harmonic rhythm and other band figures. Sometimes there will be more written in the margins describing what the band should do. Chords and Lyrics Charts should not be expected to allow the band to nail the details of a song, rather they are a general guide and are most useful when the musicians are very familiar themselves with the nuances of a piece. These charts may be transposable for musicians who know theory or can reduce the chords to numbers because they are usually used for songs with relatively simple chord progressions or often they will come from a website that offers them in any key.
Page 1 of "Wagon Wheel" by Old Crow Medicine Show (Chords and Lyrics Chart):
Chord Names Chart
This is the main kind of pop music notation used in the professional world. The Chord Names Chart of course contains all the chords in a song but also should include signature licks written out in note names with rhythms. For the band, these charts have notes about what each instrument should be doing and which are in or out during the various sections. Harmonic rhythms are shown with symbols like underlining and slashes as well as hits, pushes or other figures that can be written out. This style of notation may be transposable for trained musicians like the Chords and Lyrics Charts.
"How Come You Don't Call Me" by Alicia Keys (Chord Names Chart):
Number Chart
Often called the “Nashville Number System” because of its location of origin, the Number Chart uses numbers in place of chord names very much like music theory’s Roman numeral analysis. A lot of information can be included in Number Charts such as signature licks (also written in numbers), harmonic rhythms, hits, pushes, and other figures. There are two huge advantages to using these: they help the musician see past chord names and get the theory relationships and they are automatically transposable for any instrument in any key. This was originally developed so that instruments that make use of a Capo or different tuning can read the same chart as everyone else but it works for any instrument, even transposed ones like most horns. For the country music industry, Number Charts are the standard when communicating music to a band.
"Cornerstone" by Hillsong (Number Chart):
Conclusion
I hope this has been helpful for knowing what kind of notation will be most useful to you if you are a bandleader, composer, or songwriter. If you are a player, now you know what kinds of charts are out there, and what you will be expected to be able to read. My advice to everyone would be of course to learn how to read all of these but mainly to learn to read rhythms. Hits, underlined split measures, slashes, pushes, and figures all employ the concept of measures with beats and their subdivisions, and almost all kinds of charts utilize some kind of rhythmic notation. Thanks for reading!