Identification of:

1) Binomial distribution:

• Takes only discrete values.
• Look for finite Bernoulli trials.
• The trials are independent.
• Probability of success is fixed in any trial.

2) Poisson distribution:

• Look for a fixed range in which probability of counts of successes(discrete) is desired to be computed.
• The domain is infinite, but the range is finite.

3) Normal distribution:

• Continuous range of values.
• The shape of the probability distribution is symmetric.

4) Sampling distribution:

• Identify the measure.
• The sampling distribution is majorly identified if entities are taken from the population, and the measure is obtained over the sampled observations.

The differences between the four distributions depend on the respective identification methods and the nature of data that they describe, which are mentioned above.

Moreover, the sampling distribution of all the three deals with only sampled observations, while the other three can be described for populations or samples.