To find possible causes for this difference, try the steps below.
1) In design mode, right click on the feature then go to Properties > Visible to see if the visibility expression might allow for this.
2) In the CRM web.config file(s), see if the "ShowFeaturesEvenIfNoRights" key has been added. From the AppSettings documentation, this key is described as "If true then links, lists, and action buttons will not be automatically hidden on pages if the current user does not have rights to the feature behind the link/button. Useful for troubleshooting security because it allows you to click a link and see an 'access denied' message."