You may be operating under several misconceptions. Firstly the notation f: X->Y, putting more space to the right of the colon does occur in mathematical writing (admittedly only 1 of the 3 books I checked used that notation exclusively). Secondly that is still a labelling, you're labelling a map of a specific form (it's almost never used to label anything else, except when dealing with types but that's begging the question).

I suppose it's hard to tell the difference between labelling and stating a property, if I had to give an argument I'd say that you rarely see a formula on the left hand side, except when defining new notations (e.g. let f+g : X -> Y be the map defined by (f+g)(x) = f(x) + g(x)). Compare this to something like 'let x^2 + y^2 = 1' which kind of functions as a labelling (or omits it really) but is really more stating a proposition.

One alternative meaning in mathematics for the colon that does truly differ is using ':' as shorthand for 'such that', though sometimes people use a . or no symbol at all. This is commonly used when defining a set by some proposition e.g. { x : x \in IN and x | 2}, but also sometimes when using quantifiers.