Standard Error (SE)
Standard error describes sampling variability; a margin of error also uses a confidence level and reference distribution. A normal 95% interval uses about 1.96 times the SE.
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Margin of Error (MoE)
A margin of error needs a confidence level to exist. Quote one without it and you are off by the multiplier — about a factor of two at 95%.
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Confidence Intervals (CIs)
95% describes the procedure across repeated samples, not your confidence in this particular interval. The distinction changes how you report it.