A "HT Core" is a virtual hyperthread core, also sometimes shortened to "hyperthread". On i7/Nehalem and better CPUs, each physical core is split into two hyperthreads/HT cores through the use of SMT (simultaneous multithreading); the HT cores have their own sets of registers but share physical processing units such as ALUs, with each using resources when the other is not.
The two HT cores inside each physical core are on an equal footing and are treated the same (how each is run at any given time is determined by other logic inside the processor). It is not the case that one is a considered a true core while the other is secondary.
When one of the HT cores does not have executing instructions, as is often the case, the other one has full use of the physical core, and the performance is equivalent to having hyperthreading disabled.