Cyrillic letters and their Latin equivalences

These "equivalences" are only equivalent when transcribing the Serbocroatian Cyrillic alphabet to the Latin one. When transcribing Russian, for example, X is Kh and Ц is Ts. In Ukrainian and Belarusian, Г is transcribed as H. Well, this is all true except for J, which is only used in Serbocroatian and no other Cyrillic alphabet, and was borrowed from the Latin alphabet in place of the more usual combination of iotated characters and Й, and is transcribed in Latin Serbocroatian as J. Please clarify which particular incarnation of the Cyrillic script you are talking about and make it consistent.