To me belaying is binary. On/off. Black and white. I much, much prefer the words "ON!" and "OFF!" to this "Secure..." business, and I really wish Canadian climbing schools and guides would stop using "Secure." I have simply seen too many climbers arrive at a belay, clip into it, say "Secure" and then expect to be lowered off while their belayers are off having a smoke or whatever. "Secure" also sounds a lot like "need beer," "send gear," "Oh Dear," "Can't hear," etc. etc. "OFF!" is a terse, single-word sound that's hard to confuse with anything, and has only one meaning, ever.
"Secure" has an implied meaning; the belayer has to figure out what the climber means. "OFF!" from the climber means he's OFF, no more belay required. The meaning is clear in the word. Saying "Secure" is like yelling, "Falling Object!" Yelling, "ROCK!" makes a hell of a lot more sense, and that's why we use it. "OFF!" is like "ROCK!" The meaning is clear in the word, you don't have to ponder what is meant (unless you're a linguistics nerd or philosopher).
Safe climbing with a partner is often about communication, and many climbing accidents occur because of poor communication. Why use a vague word when there is a concise alternative?
"Secure" is also rather wussy, a sort of Morrisey-style word that sounds kinda whiny and unsure of itself, like a self-help session for insecure leaders. I mean, if you're "secure" now then you must have been "insecure" earlier, yeah? Sorry about that, get over it and use "ON!" and "OFF!" for god's sake.
I'm on a mission to get this word chucked out of our Canadian climbing lexicon. "Secure" is a word thought up by an verbally insecure desk-riding bureaucrat. "OFF!" is a word thought up by a climber 'cause it works.
PS--and, if in doubt, always leave the climber on belay. Worst-case scenario you have to feed the entire rope through your belay device. That's a much better worst-case scenario than taking the climber off because he or she uses some BS "secure..." and then gets dropped on his not-so-secure head.