The U.S. Food and Drug Administration sets specific guidelines on what must be included in a vaccine package insert. Specifically, any side effect that occurred after receiving the vaccine during the clinical trials must be reported, even if that side effect was reported as occurring at a similar rate among people who received the placebo.
Data collected during clinical trials are given to the Centers for Disease Control and Prevention (CDC) to help them make vaccine recommendations to healthcare professionals. The CDC looks specifically for side effects that happen more often in people who received the vaccine than those who received the placebo. Only side effects that happen more often in the group that received the vaccine, in comparison to the group that received the placebo, are listed on the CDC website as possible side effects.
This is why the package insert and the CDC list may have different side effects for vaccines. The FDA requires all side effects to be reported on the package insert, even if they happen as frequently among the placebo group during clinical trials.