I understand the poission approximation to the binomial distribution:

$\displaystyle e^{\lambda}{\lambda^k \over{k!}}$

where $\displaystyle \lambda=np=$mean number of success in a given population of size n

But I am confused how it is mapped to the Poission distribution:

$\displaystyle e^{\lambda t}{(\lambda t)^k \over{k!}}$

where $\displaystyle \lambda t=$mean number of success in a given population of size n

Now, how can $\displaystyle \lambda$ and $\displaystyle \lambda t$ mean the same thing???