Or that's what we call them in mathematics. If you use parentheses around the arguments of a function, I think this would remove any concern over "or" vs. "||".
Like this:

open(FH, "filename.txt") || die "$!";
 # OR
open(FH, "filename.txt") or die "$!";
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Functionality should be identical in the two cases above, no? Of course, this is only for calling of functions or something like that. It doesn't work the same with other above-mentioned examples such as

$a = $b || $c;
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Which is an entirely different sort of thing.