Translate Drupal's built-in English to another kind of English
You can do this with the Locale module, which is provided by core.  Steps are for Drupal 7.  This assumes you want to completely replace the built-in English with your own custom version of English (which will still show the strings for the built-in English unless you have translated/edited them).


Enable the locale module.
Go to languages admin (/admin/config/regional/language).
Click edit for the English (built-in) language.  Add en as the Path prefix (this will allow you to add your own language without a path prefix.)  Save.
Click "Add a language"
Choose "Custom language", set a language code, set both language names to English,  leave Path prefix and Language domain blank, and choose Left to right for the Direction.
Go back to the language list (/admin/config/regional/language) and set your new English as the default language.  Then uncheck Enabled for the built-in English.
Translate all the strings you want to modify on the translation screen (/admin/config/regional/translate/translate).