To modulate in regular music theory means to change key. But in synthesizer programming it means to change a value over time. So for example you'd say that an ADSR envelope can modulate an instrument's volume over time. Or an LFO that modulates the cutoff frequency of a lowpass filter.
So just wanted to make sure that these are different terms?
Yes, the same word has different specific meanings in those two contexts - you've described both meanings well i think!
The original Latin root of the word simply meant "to regulate" or "to measure."
The first musical use of the word (in 14th century France) simply meant "to sing a song" - and presumably, to keep in time and in tune while doing so.
The meaning of "to change key" came later, in about 1750. Of course before that time the modern concept of a musical "key" didn't exist, so this was a new name for a new idea.
The meaning relating to controlling electrical signals dates from the 20th century and the start of commercial radio communication. The usage describing synthesizers (which first appeared in the 1960s) was a natural extension of that.
modulation means change the mode:
there are many modes you can change, in our language (German and French) "mode" means the same as fashion.
As the fashion "mode" changes every season, some politician change their meaning like their shirts ... and also the political mainstream is changing like the modes and fashions (s. political correctness)
On the synthesizer you can modulate the ADSR - as you say.
In harmony and music modulation is changing the mode or key, changing the tonality or tonal center. Thus your concepts are correct.
