To describe "Special" and OVA, we need to describe what's "normal" anime.
Usually anime (TV series anime) is broad-casted weekly.
It will continue 13 or more weeks.
It's usually free with Television advertisement (and has eye-catch at center of episode).
TV station have their code: no pantsu scene, no violence scene.
The DVD (or BD) will be release later.
Special (aka TV Special) is not weekly. Usually yearly or one shot.
It's have only one episode but it's have longer length (ex 2 hours).
It's still intended for broadcast. Need to meet broadcast code.
OVA is created for selling (by Video or DVD).
It's intended to the small number of viewer without advertisement.
It means more otaku friendly theme.
No need to follow broadcast code. It's OK to have hard violence scene.
But, in recent time, some OVA was broadcasting with censorship.
On the other hand, some TV series is on air with censorship, and selling DVD (or BD) without censorship version.
The boundary became ambiguous.
Other category is anime movie which is intended to show in theater.
Anime movie is between special and OVA.
The anime Lupin the Third has all TV series version, OVA, Anime movie and TV Special.
In this case, special version is yearly release.