- "Descent, a crossing over, incarnation, exhibition into human form"
In Hinduism, it is believed that Vishnu incarnated on Earth in various forms at different points of time/in different Ages. The most popular avatars of Vishnu include Ram and Krishna. In these cases Vishnu took birth through mothers' womb. But in case of other avatars in animal or other forms he is believed to have just appeared in that form suddenly. For example the Vishnu's incarnation as a fish (matsyaavataar) or half man-half lion (narsimhaavataar).
When compared to such incarnations (either by taking birth or sudden appearances) of Vishnu, the incarnation of Shiv as believed by BKs/PBKs is not an incarnation as such because Shiv neither took birth nor appeared suddenly as God. Since it is believed by the BKs and PBKs that the Supreme Soul enters in Dada Lekhraj and Baba Virendra Dev Dixit respectively and did not take birth as these two personalities, the revelation of Shiv through these personalities cannot be termed incarnation/avatar from a classical Hindu point of view. That is why BKs/PBKs use the term 'divine incarnation' (divya avataran), 'entry into another being' (parkaya pravesh), etc. to describe the incarnation of Shiv.
Regards,
OGS,
Arjun