How to make a custom function as inbuilt

Question

I have a custom function like following:

SyntaxInformation[
   TwoNumberSameQ] = {"ArgumentsPattern" -> {_, _, OptionsPattern[]}};
Options[TwoNumberSameQ] = {ShowDifference -> False};
TwoNumberSameQ[x_, OptionsPattern[]] := {x, 
  OptionValue[ShowDifference]}
TwoNumberSameQ[a_, b_, OptionsPattern[]] := 
 If[OptionValue[ShowDifference], 
  If[a === b, True, {False, Abs[a - b]}], If[a === b, True, False]]

Usage:

TwoNumberSameQ[3,4]

False

TwoNumberSameQ[3,4,ShowDifference->True]

{False, 1}

 TwoNumberSameQ[3,3]

True

I have some dissatisfaction to this function.But the documentation have a little relative explanation for this area.

Question one

How to make the option have a black color like as a in-built function,but blue like:

Question two

How to make TwoNumberSameQ's definition more concise.I just test one option but result so many repetitive code.I cannot imagine how mess when I set three or more option.

Addtional quesiton

If I can make the option have some optional values to choice.I'll be happy more. :)

Answer 1

1. Global` symbols are blue unless they have a value but if you use any other context that is on $ContextPath the symbol color will be black just because it was created.

   So use System` by mentioning option name when it is parsed for the first time:

   Options[TwoNumberSameQ] = {System`ShowDifference -> True}
   

   or define your function in Begin/EndPackage where the option name is exported. Keep in mind conflicts so choose your names wisely.

   BeginPackage["Numbers`"];
   
     TwoNumberSameQ; ShowDifference;
   
   Begin["`Private`"];
   
     (* your definitions *)
   End[];
   
   EndPackage[];
   

I believe rest of your questions was already answered in:

2. How to specify and use nested options for a function?

   How to deal with the condition that a function own many options?

   Writing functions with "Method" options

3. Prompt a set of possible options