Well, paul, that
tito, technically thare are Dual Core CPU's, Core2 Duo CPU's, and most confusingly Dual-Core CPU's.
These originally designated three different chip families, but now they are pretty much grouped into "Dual-Core" now.
It is almost simpler to talk about names (Allendale, Conroe, Wolfdale) or designations (E2180, E6600, E8400). Except there are two E6600's (Conroe @ 2.4 GHz and Wolfdale @ 3.0 GHz).
Intel has not done us any favors.
"dual core" (lower case) is an adjective describing a CPU with two cores in a package. The others are trademarked brand names.