No, HSTEd has got it right in essence. The High Speed Diesel Train project was intended as a stop gap measure until electric APT trains were rolled out; starting with the West Coast Main line, and then probably looking to electrify the East Coast later which of course did happen, but a little later than was probably intended. The HSTs would then be relegated to secondary duties (Such as Transpennine and Edinburgh to Glasgow, for which HSTs were originally proposed). The APT team at Derby was, however, quite distant from the team working on the development of the HST, so you are right in saying that they were separate projects.
APT development was an incredibly long and protracted process: Reference was first made to the production of a 150mph capable "Advanced Passenger Train" in late 1966, and the developmental APT-E was rolled out in 1972, at pretty much the same time as the prototype HST set was finished. It was the pre-production APT-P trainsets that came about later, in 1979.
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Beat me to it