Differences and relations between high-performance/throughput computing and parallel computing?
As noted by @JukkaSuomela, you can do parallel computing on low-end resources such as your laptop and even on your mobile phone (if they are equipped with a multicore processor). However, HPC (High Performance Computing) is, roughly stated, parallel computing on high-end resources, such as small to medium sized clusters (ten to hundreds of nodes) up to supercomputers (thousands of nodes) costing millions of dollars. Therefore, the difference is mainly in the hardware used. 

Finally, HTC (High Throughput Computing) refers to executing the maximum number of tasks (or jobs if you prefer) per time unit. A classical example of HTC computation is the so called parameter sweep, in which you must run the same executable, but varying in each execution a set of parameters (thus the sweep spans the whole parameter space).