I don't really understand the difference between exponential and geometric distribution.
Did you try looking at Wikipedia?
The exponential distribution may be viewed as a continuous counterpart of the geometric distribution, which describes the number of Bernoulli trials necessary for a discrete process to change state. In contrast, the exponential distribution describes the time for a continuous process to change state.
Exponential distributions involve raising numbers to a certain power whereas geometric distributions are more general in nature and involve performing various operations on numbers such as multiplying a certain number by two continuously. Exponential distributions are more specific types of geometric distributions.
Exponential distributions: 2, 4, 16, 256 or 3, 9, 81, 6561.
Geometric distribution: 2, 4, 8, 16, 32, 64.
Just my two cents anyway.