Every one of my lecturers have always called it this, as do I, despite the fact that I know its properly called 'tilde'. Does anyone have any clue where this convention comes from and why it might have became (somewhat) standard?
I'm not convinced they are exactly the same, as a tilde is an accent mark over a letter, while a twiddle is a relationship operator sitting between letters (or numbers, or whatever).
But you might as well ask why an exclamation point is referred to as "bang" and as "splat" by various software (and math) people. And don't get me started on the ridiculous renaming of "poundsign" to "hashtag" . (Insert rant about misusing pound sign vs. number sign vs. musical sharp sign -- yes, they are not the same symbol)
The OED gives a citation for the noun "twiddle" possibly meaning the tilde sign dating to 1894:
‘e’ for ‘æ’ is just as much a contraction as ‘r’ with a twiddle for ‘rum’.
This might or might not be a description of an "r" with a tilde, analogous to "u" with a tilde meaning "um" which I have seen in 16th century printed books.