Their kinds differ

module type LOG = sig
  type level =
    | Debug
    | Info
    | Notice
    | Warning
    | Error
    | Fatal
end

module type S = sig
  type log_level =
    | Debug
    | Info
    | Notice
    | Warning
    | Error
    | Fatal
end

module Make (Log : LOG) = struct
  type log_level = Log.level
end

module Log_lwt = struct
  type level = Lwt_log.level
end

module M = Make (Log_lwt)

(*

Error: Signature mismatch:
       Modules do not match:
         sig type level = Lwt_log.level end
       is not included in
         LOG
       Type declarations do not match:
         type level = Lwt_log.level
       is not included in
         type level = Debug | Info | Notice | Warning | Error | Fatal
       Their kinds differ.

*)