Yes, this is often a confusing issue in Alpha Phi Alpha as well. Our "coat of arms" is properly called "The Fraternal Design."
I ALWAYS call it the Fraternal Design, not only because that's how I was taught, but because when you say Fraternal Design, there should be no mistake.
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The Shield of the Fraternity is used on shingles, official correspondence, banners, etc -- any official fraternity thing used by officers or chapters to represent the organization and IS NOT wearable.
Most people call this the shield. But is it really a shield? I don't know. I often call it the "seal" because of its uses, but that may be wrong too.