Different transmissions for reciting various versions of a same mantra acc. to any of Vajrayana branches
This is a very partial answer because I can provide no textual reference.

Differences between mantras of the same deity are of two types:


In terms of length (short version / long version)
In terms of category


For instance: Vajrasattva has (1) a short mantra, (2) a long mantra, and (3) a mantra associated with its wratful aspect, that is another category, such as 'Heruka Vajrasattva'.

Generally, there is no objection for practitioners who received an initiation to recite both short and long version of a mantra of the same deity. As to reciting the mantra of another category/aspect of that same deity (in the given example, that of Heruka Vajrasattva), you must ask your teacher. In Kopan monastery - and so Kyabje Lama Zopa Rinpoche - they do allow one to recite Heruka to those who took just Vajrasattva. If you are not a student of his, ask your own teacher.