They are absolutely entirely different operations - And TKHF is not a "contract" - It's an in house operation run and staffed by the Royal Travel Office.
I'm just unsure about which one it is that Nowherespecial is referring to with his suggestion that "The Royals" are getting a 139.
The MOD statement above seems pretty specific that they are dropping the 32 Sqn helicopter role. To then decide to replace it with a significantly larger aircraft seems a bit odd.
I was wondering if TKHF had decided to replace one or both of their 76's - XXEB as you said and XXED - with a 139.