Related yet different, here’s how…
A quick note on the “preliminary terrors” of notation:
 e is Euler’s number – you’ll find the e on your calculator or the EXP() function in Excel
 The parameter is conventionally written as λ (pronounced lambda).
Poisson 
Exponential 
Number of events that occur in an interval of time  Time taken between 2 events occurring 
For example… the number of Metrorail trains that arrive at the platform in an hour  For example… the time between one Metrorail train arriving and the next 
6 trains  10 minutes between trains 
The random variable is discrete – this is a countable number of things that happen  The random variable is continuous – typically time, but may represent other factors like distance 
l represents the number of events (per unit of time)  l represents time between individual events 
Graphically, a Poisson distribution looks like this:  Graphically, an Exponential distribution looks like this: 
Calculate probability as follows:
P(X=x) = e^{–}^{λ}λ^{x} / x! 
Calculate probability as follows:
P(x>n) = e^{–}^{λ}^{(n)} P(x<n) = 1 – e^{–}^{λ}^{(n)} P(n<x<m) = P(x<m) – P(x<n) 
On average 6 trains arrive at the platform per hour… 

What is the probability that fewer than 2 trains arrive in the next 20 minutes?  What is the probability that a train arrives every 8 minutes or less? 
λ = 2 per 20 minutes  λ = 0.1 per minute (6/60) 
P(X<2) = P(X=0) + P(X=1)
= e^{–}^{2}2^{0} / 0! + e^{–}^{2}1/ 1! = 0.41 
P(x<8) = 1 – e^{–}^{0.1(8)}
= 0.45

2 amazingly simple video tutorials are available on YouTube if you need a quick walkthrough: