What is the correct terminology usage regarding "downconversion" and "correlation"?
Downconversion always involves multiplication with a simple periodic signal, such as a single frequency sine or square wave. The purpose is to reduce the high frequency signal down to something lower that can be managed more easily. This rarely comes right down to DC, an IF output is usually used, bandpass filtering the output of the mixer. The mixing frequency is chosen to be something other than the input centre frequency.
Correlation is more general and involves multiplication with an arbitrary signal, which is usually non-sinusoidal, such as a Walsh function, or an m-sequence. The purpose is to extract signals of the same shape as the reference waveform, and usually comes right down to DC, lowpass filtering or integrating the output of the mixer. The reference waveform is chosen to match the expected input.
A conventional diode ring, double balanced, RF mixer is generally good enough for downconversion. Correlation usually happens at lower frequencies when mixers that can better handle wideband arbitrary signals are used, which these days are digital multipliers, once the IF signal has been digitised.