GHCi's :t alleges these three data constructors have the same type :: Int -> T Int (modulo name of the type constructor):

data DG a where MkDG  ::            Int -> DG Int 
                MkDG2 :: (a ~ Int) => a -> DG a

data family DF a
data instance DF Int where MkDF ::  Int -> DF Int

I tried switching on verbosity flags, but to no avail: -fprint-explicit-foralls, -fprint-equality-relations, and a few others.

The DG constructors are GADTs, the DF constructor is not. So it's not hard to see different type-level behaviour:

f (MkDF  x) = x                   -- accepted without a signature
-- f :: DF Int -> Int             -- inferred signature, or you can spec it
-- f :: DF a   -> a               -- rejected: signature is too general/
                                  -- a is a rigid type variable

g (MkDG  x) = x                   -- } without a signature, rejected
g (MkDG2 x) = x                   -- } "untouchable" type (Note)

-- g :: DG Int -> Int             -- } g accepted with either sig 
-- g :: DG a   -> a               -- } ?but MkDG doesn't return DG a, allegedly

Note: at least the error message re MkDG2 does show its type as :: (forall a). (a ~ Int) => DG a -> a. But doggedly MkDG :: Int -> DG Int.

"Untouchable" error messages are a fertile source of questions on StackOverflow. The message does say Possible fix: add a type signature for 'g', but gives no clue what the signature might be.

If you've imported these data constructors from a library, such that you can't (easily) see they're GADTs, couldn't :t give you better help to show what's going on? Or should one of the verbosity flags already do this?