I don't know much about Advaita Vedanta and little about Buddhism, however Encyclopedia Brittanica has this to say about Buddhism;
'anatta, (Pali: “non-self” or “substanceless”) Sanskrit
anatman, in
Buddhism, the doctrine that there is in humans no permanent, underlying substance that can be called the
soul. Instead, the individual is
compounded of five factors (Pali
khandha; Sanskrit
skandha) that are constantly changing. The concept of
anatta, or
anatman, is a departure from the
Hindu belief in
atman (“the self”). The absence of a self,
anicca (the impermanence of all being), and
dukkha (“suffering”) are the three characteristics of all existence (
ti-lakkhana).'
Source:
Anatta | No-Self, Non-Attachment & Impermanence
What I'm basically taking away from this is that anatman is a departure or difference from the belief in Atman of the Hindus (ie not essentially the same teaching) and that the "Impermanence of all being" is one of the "charectaristics of all existence". In other words there is no none transient thing if I have understood correctly.