Technically a variety, but not a die variety or error. Just a design variety like a type 1 SLQ or a type 1 Buffalo.
Variety, but why @ 16M mintage it is priced higher than the 'No cents' variety @ 5.5M mintage escapes me.
Because everyone thought the no cents version was going to be rare or recalled so everyone hoarded them while they just spent the with cents coins. So now today the no cents type is readily available in nice condition and the with cents are all worn out or were lost/ redeemed and recoined etc over the years.
Don't take um-bridge at my post. Sounds like a well thought out response. Your numismatist grandfather told you, right?