As a general rule, as with everything else on VocaDB, information that is already provided in one way usually does not need to be repeated in other ways.
Original songs ("オリジナル曲" in Japanese) are songs that are completely original content and aren't based on other songs.
Note that on VocaDB self-covers and self-remixes, made by the artist him/herself, are to be classified as covers and remixes, not "original songs", unlike on NicoNicoDouga.
Sometimes the producer might publish multiple different versions of a song, usually with different vocals or different lengths, calling all of them originals. The songs might be published in different media, for example an album song vs. NicoNicoDouga upload. To avoid misunderstandings, as a rule of thumb the version that was published first, regardless of medium, should be considered the original, and all others are derivatives. There are exceptions to this rule, for example if the earlier version is officially labeled a cover or if it's commonly agreed that way.
Extended ("long") versions of songs should generally be separate from the original song entry on VocaDB, unless the short version was intended to be only a demo, in which case it can safely be replaced by the longer version. Extended versions should generally use the cover type.
Instrumental song that is an original, meaning it's not an instrumental version of some other song, should be classified as original song, not instrumental. Instead, you should indicate that the song is an instrumental by using the instrumental tag.
As an important exception, please note the Drama PV song type.
Remaster ("修正版" or "リマスター版" in Japanese) means an improved/remastered version of a song. Sometimes artists may replace the original song with a remastered version, even deleting the original.
Sometimes the artist remasters the song for an album release. Quite often album versions of songs are remasters, but this is not always the case.
In order to use the remaster song type the song should sound almost identical to the original, with the general melody and song structure intact.
Cover is a re-recorded version of a song. Most commonly in the Vocaloid/UTAU world covers are used to record the song with a different voicebank from the original, keeping the instrumentals intact. Sometimes a cover is another artist's interpretation of the song, in which case it might sound almost identical to the original.
Remix is an edited version of the song, usually made to sound quite different. The remix is often different musical genre from the original. This song type should also be used even when the remix was made by the original artist. In this case you should add the self-remix tag.
Songs that are called arrangements should usually be classified as remixes on VocaDB.
Remix or cover?Admittedly, the difference between a remix and a cover is often hard to define, and usually this doesn't matter very much, as these two types are functionally identical on VocaDB.
All other things being equal, try to figure out what the intention of the artist was when they made the song.
AKA off-vocal or karaoke.
Instrumental song type should be used for one purpose: instrumental versions of songs, when a non-instrumental version with vocals is the original. This means, just like cover and remix, instrumental should always be a derived version.
The music PV type is used for remarkable PVs of original songs. By creating a separate entry for the PV the animator and other people involved can be credited accordingly, and things like the MMD models used can be indicated with tags. Sometimes the PV might be more well known than the originally published version of the song, for example the Sweet Devil PV by wakamura and Love is War.
Like with most other song types, music PVs should always be derived versions. If the song was originally uploaded/published with the PV, that PV should be included with the original song entry.
Drama PV is an animation where the main focus is story instead of music. Most commonly these are made with the MMD software ("MMD Dramas").
Note that unlike with the other song types, the drama PV type should always be used when a PV is considered drama. This is because the other song types are used to represent music, while the content of drama PVs is fundamentally different. Drama PVs are almost always originals, there are very few derived dramas.
Mashup is a song that is made by blending two or more songs