as i understand in suttas
birth or rebirth
it is arising in this or that state, (in a state o deprivation or a state of devas)
but the Buddha view that this is inconstant, and suffering.
reincarnation is i understand is continues from state to state, and does not change. it has a view that this is permanent.
if veiw of permanent was true, we would not suffer. but it is false view. you can't get what does not exist. ( it is not a characteristics of existence)
so some people has a view that it is not this way but it will naturally become this way.
or it is not this way but i will make it this way.
by this they have a wrong view that i suffer now,but when i go to heaven i will live for eternity.
ignoring the fact that all realms follow the same laws of existence.
Kamma is the means by which we take this or that state of arising.
Kamma is not self but we are still subject to it results
because a law of not self does not cancel out the law of kamma.