You may want to check out this document from the FAA also linked in that document is this document which may shed more light on the matter
The general qualifications for an Instructor Rating require you have a
combination of experience, knowledge and skill. Title 14 of the Code
of Federal Regulations (14 CFR) part 61 requires that pilots must be
able to read, write, speak, and understand the English language. If
you cannot meet these requirements of English fluency, an airman
certificate cannot be issued. For medical reasons, an appropriate
limitation may be placed on the certificate.
You must pass the Fundamentals of Instructing Knowledge Test and a Flight or Ground
Instructor Knowledge Test specific to the instructor rating sought.
You may take these tests on the same day, and you do not have to take
them in any particular order. An instructor rating obtained by passing
the Military Competence Instructor (MCI) exam does not require the
candidate to take the Fundamentals of Instructing (FOI) exam.
applying for any additional instructor rating, you are not required to
take the Fundamentals of Instructing Knowledge Test again. Once you
have acquired a Flight Instructor Certificate, you are eligible to
give ground instruction required for a Pilot or Instructor Certificate
or rating, based on the ratings on your Flight Instructor Certificate.
Because of this, it is not necessary to obtain a separate Ground
Instructor Certificate since you would already have these privileges.
AskACFI breaks it down nicely here.