Mean of exponential = 1/
Variance of geometric = (1-p)/p2
Variance of exponential = 1/2
Therefore, if (the instantaneous rate of events per time unit) is equal to p (the probability of an event in a given time unit) and if p is small, then the geometric and exponential distributions converge.
This makes sense, since if p is small, then there should be little difference between observing events over specific time periods (eg every day) or continuously over time. When the event will first be seen is roughly the same in either case.
In contrast, if is very large, you could see an event instantaneously in the continuous case, but you would have to wait for one time unit to pass in the discrete case.
[Notice that as goes to infinity, E[X] for the exponential distribution goes to zero. But as p goes to one (its maximum) E[X] for the geometric goes to one.]