They're entirely unrelated. HyperThreading is about virtual cores. Basically, when a (physical) core is under-utilized, the CPU can interleave data from another thread into the current one, milking a little more out of it. This gives the CPU 8 virtual cores (starting from 4 physical), when HT works correctly you can get about 20% more perfs out of your CPU, but it's pretty rare to have the perfect HT workload. Usually nothing to write home about.
Turbo Mode is a feature of the i* CPUs (i5, i7): when not all the cores are used and the CPU is cool enough, it can overclock itself dynamically. For the i5 750, this means that if you're using only 1 or 2 core your 2.66GHz quad-core can become a 3.2GHz dual-core. On i7 860 (2.8GHz), if you use 2 cores the CPU can go at 3.33GHz, and a single core can ramp up to 3.46GHz. It basically means your quad-core is much more flexible and works much better on single and dual-core loads.
They are
Handbrake is highly threaded so turbo mode won't activate beyond level 0(*) (it should always be able to load all 4 cores at the same time). I don't know how Handbrake behaves under HT so I can't comment on that one.
*: if the cooling is good enough, turbo mode actually overclocks the CPU even when all 4 cores are loaded: the i5 750 will run at 2.8GHz rather than 2.66, and the i7 860 will run at 2.93GHz instead of 2.8.