They are probability distributions!
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The Poisson distribution is discrete.
Half the discrete unit.
A discrete probability distribution is defined over a set value (such as a value of 1 or 2 or 3, etc). A continuous probability distribution is defined over an infinite number of points (such as all values between 1 and 3, inclusive).
If the question is asking if a continuous distribution can be converted to a discrete distribution, the answer is yes. Your age has a continuous distribution but in most cases, the information is recorded and analysed as if it were the whole number of years - a discrete distribution.
You may need to make a continuity correction - see statistical text books for details.