Both expressions mean "nervous," yes, but while "ill at ease" literally implies sickness, "butterflies in the stomach" doesn't necessarily have to be an unpleasant sensation. "Stage fright," or the fear an actor, speaker, etc. experiences just before going on, is often called "butterflies," but a person might also experience "butterflies in the stomach" before a wished-for event, such as opening an envelope containing what you hope is a big check.
You could say, "When her boyfriend dropped to one knee and took a small box out of his coat pocket, Marybelle felt butterflies in her stomach," but you wouldn't use "ill at ease" in the same way. (Unless, of course, Marybelle didn't want to marry the guy and wondered how she was going to tell him no!) :)
[not a teacher]
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