It's a Poisson process, with a mean of 10 minutes. So...
It's actually not a Poisson process (poisson = discrete number of events in fixed time interval, exponential = continuous time intervals between single events) but they're closely related.
Poisson distributions either use fixed time intervals or probabilistic average rates. Bitcoin is the latter.
https://en.wikipedia.org/wiki/Poisson_distributionIn probability theory and statistics, the Poisson distribution (French pronunciation [pwasɔ̃]; in English usually /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the
probability of a given number of events occurring in a fixed interval of time
and/or space if these events occur with a known average rate and independently of the time since the last event.
Indeed, Poisson = the probability of a given number of events. Number being a
discrete amount (0, 1, 2, 3, etc). Whereas exponential = the probability of the time or space between two subsequent events. Time or space being a
continuous (real number) amount. Like I said, they're closely related (both deal with a known average rate, amongst other things), but the Bitcoin mining block time is really exponentially distributed.
The most important distinction between Poisson and Exponential is being a discrete vs continuous probability distribution.