Question: are standard error and margin of error the same?
Answer: For a sample of size n=1000, the standard error of your proportion estimate is √0.07⋅0.93/1000 =0.0081. The margin of error is the half-width of the associated confidence interval, so for the 95% confidence level, you would have z0.975=1.96 resulting in a margin of error 0.0081⋅1.96=0.0158.