Interesting nitpick, but I must be missing your point somehow.
>They are the same thing
No, that's in fact not the same characters (obviously?), even if they can be used to represent the same phoneme and could thus be viewed as interchangeable. I've made it explicitly clear my comment concerned spelling though.
>when you don't use latin characters.
I have no idea how to parse this, given that all three of them are letters used in latin script. I suppose one of them wouldn't be considered part of the basic latin alphabet, but then your sentence still doesn't make sense to me.
In German characters, there is now difference between 'sz' and 'ß'. 'ß' is in fact just the concatenation of the glyphs of 's' and 'z'. 'ß' only became relevant when the glyphs switched to Antiqua.
I don't know it German characters are considered to be Latin script or not. The number and meaning of characters is mostly the same, besides stuff like 'ſ', but the glyphs are all different.