Do any people distinguish between "analog" and "analogue"?
In my personal usage, the words "analog" and "analogue" are allocated to two different meanings of the word.
One refers specifically to non-digital signals, for example:
The analog clock reads 5:37.
The phonograph only works with analog signals.
While the other is used in the sense of reference to another material:
The remotely activated webcams built in to laptops are a chilling analogue to the telescreens in George Orwell's 1984.
I have a similar split between "dialog" and "dialogue", which refer specifically to a message window on a computer GUI and spoken conversation respectively.
However, in all the language packs for software that I've ever encountered, the words will always exclusively be analog and dialog or analogue and dialogue, for American and British English respectively. Similarly, when I see most people type these words, they will usually use "dialog" to refer to spoken conversation and be American, or use "dialogue" for the message window and be British.
My question is, is this analog/analogue split a regional variation in Canadian spelling, or is it just something I've picked up personally? Does anyone else, or any other group of people, make this distinction?
Dialog vs dialogue and analog vs analogue are simply spelling differences, and are not recognized in any major dictionary (that I was able to find) as having distinct definitions.
Technological vocabulary, specifically related to electrical and computer engineering, prefers the shorter forms, and because of this we are seeing those forms being adopted in places where the more traditional form would otherwise be preferred.
My guess is that this is similar to the distinction drawn between theater and theatre, where some American speakers in the theater community treat the words as being distinct, though no formalized or widely recognized distinction exists.
While many on both sides of the Atlantic don't make a distinction for the context, you're certainly not alone in making that distinction. For example, see http://grammarist.com/spelling/analog-analogue/
As a fellow Canadian, I have to make decisions about when to use British and when to use US spellings, due to the fact that we're relatively free to choose, aren't we. As a result, I/we probably come across these distinctions more often than people who don't check because they feel bound by their national spelling. I like it, and find it useful, when such differences can be used to distinguish meanings or contexts. Why not preserve the nuances, I say! So, yes, preserve the distinction.
Some words come from the French and have changed spelling when passing into the English language, sometimes in the States and not in Britain, e.g. center (USA) and centre (British and French). This is the same for analogue which is a French word that has the same meaning in French and English