Are margin of error and sampling error the same

Yes they are 
When a research question asks you to find a statistical sample mean (or average), you need to report a margin of error, or MOE, for the sample mean. The general formula for the margin of error for the sample mean is the population standard deviation, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence

1.Find the population standard deviation and the sample size, n.
2.Divide the population standard deviation by the square root of the sample size.
3.Multiply by the appropriate z*-value.
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