This typechecks:

{-# LANGUAGE TypeInType #-}

import Data.Kind

type Id (a :: Type) = a

data Foo :: Id Type

But changing the type synonym to a type family causes it to fail:

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeInType #-}

import Data.Kind

type family Id (a :: Type) :: Type where
  Id a = a

data Foo :: Id Type

$ ghci Foo.hs
GHCi, version 8.2.1: http://www.haskell.org/ghc/  :? for help
Loaded GHCi configuration from /home/rgscott/.ghci
[1 of 1] Compiling Main             ( Foo.hs, interpreted )

Foo.hs:9:1: error:
    • Kind signature on data type declaration has non-* return kind
        Id *
    • In the data declaration for ‘Foo’
  |
9 | data Foo :: Id Type
  | ^^^^^^^^

That error message is wrong, since Id * = *. And, besides, the definition should be accepted.

EDIT: This was originally about the error message. But #14042 (closed) changes the goal of the bug to fix the behavior.