Kr808d-2 (or E9) is not compatible but these are rare.
In my experience items described as '808' are d-1 compatible. You're pretty safe there.
Kr808d-m3 is compatible with d-1, it's a slightly thicker battery (12mm) sometimes described as a mini vgo or slim ego. Elite 808 from cigeasy.com is this style but you can get it unbranded for way cheaper elsewhere.
Kr808-dm1 (I think) is like the m3 but longer/higher mah. This is just as I understand, I haven't researched this one much.
Is that what you were after?