"... the Core and Core 2 were totally different than the Pentium 4 and Pentium D (processors that up until now I had the perception of being the modern day version of the Celeron or Sempron). " ==> The Core architecture chips are indeed substantially different than the Netburst architecture used in the Pentium 4 and Pentium D CPUs. But the Pentium 4 and Pentium D's are NOT the "... modern day version of the Celeron ..." ==> indeed they were the premium chips of their day; and the Celerons were the lower-end versions of the Pentiums.
However, the current Pentium Dual-Core CPU's are core architecture based CPUs -- the same as the Core 2 Duo's. They are simply Core 2 Duo's with less cache and without hardware virtualization support. There are 15 models of these "Pentium Processor for Desktop" CPUs:
http://processorfinder.intel.com/List.aspx?ParentRadio=All&ProcFam=2841&SearchKey=These Pentiums, however, have no relation to the earlier Pentium processors -- it's simply Intel bringing back the Pentium name for its brand recognition.
"... now I'm hearing that "The pentium core duo is the same thing as a core duo" " ==> True, for the "Pentium Processor for Desktop" CPUs I noted above. Same architecture, same features EXCEPT for the smaller cache and lack of VT support. In a sense, you could think of these Pentiums as the "Celerons" of the Core 2 family. But they're not "dumbed down" in any way ... they are still excellent performers => for example, a Pentium Dual Core E6300 scores 1838 on PassMark's CPUMark (an excellent benchmark of CPU "horsepower"). This is better than many of the lower-end Core 2 Duo's, and FAR better than any earlier Pentium CPUs. The BEST Pentium-4 (3.8GHz) scores 624, and the best Pentium D (3.73GHz) scores 1261.
"... A "Pentium Dual Core" is a PENTIUM, and a "Core Duo" is a CORE. Is that correct? " ==> No. As I noted above, both the Pentium Dual Core and the Core 2 Duo CPUs are core-architecture chips with the same fundamental design.
