# Relationship binomial distribution and central limit theorem + poission distribution

From the central limit theorem the binomial distribution can be approximated by a normal distribution N(0,1). But the binomial distribution can also be approximated by a poisson distribition.

Does this mean there is a relationship between the normal distribution and the poisson distribution (especially as n->infinity in B(n,p))?

I'm confused about this. To me it sounds like the normal distribution and the poisson distribution are equal then. Or does the standardisation in the central limit theorem make the difference?

Thanks