Nobody coined those two terms. Both are scriptural terms. They are found at many places in various Puranas.
Couple of such references from the Devi Bhagavata Purana (DBP):
141-159. Thus I have described to you the nature of Prakriti. So in
this Punyabhumi Bharata Varsa, to worship the Devi is by all means
desirable. In days past by, the King Suratha worshipped the Mula
Prakriti Durga, the Destructrix of all evil. Then again Sri Rama
Chandra worshipped Her when he wanted to kill Ravana. Since then Her
worship is extant in the three worlds.
He who gives his whole property to a Brahmin, gets in the end four
times that ; there is no doubt in this. He who gives Jambu Dvipa to an
ascetic Brahmana, gets undoubtedly in the end one hundred times the
fruit. If you give away Jambu Dvipa, the whole earth ; if you travel
all the Tirthas, if you perform all sorts of asceticisms, if you give
shelter to all, if you make gifts of all sorts, know that you will
have to come again to be reborn in this earth ; but if you become a
devotee of Mula Prakriti, then be sure that you won't have to come
here and be reborn.
So, those two terms existed in the scriptures much before Ashoka's era.
Couple of more references from the same Purana:
0 Child! Now hear about the seven Dvîpas and the seven Oceans :-- The first is the Jambu Dvîpa; the second is Plaksa, the third is
S'almalî; the fourth is the Kus'a Dvîpa; the fifth is Krauncha; the
sixth is the S'aka Dvîpa; and the seventh is the Puskara Dvîpa. The
second Dvîpa Plaksa is twice the first Jambu Dvîpa and so on; each
succeeding Dvîpa is twice as large as its previous one.
[Lord Vishnu said] O Gange! You will also have to take incarnation
in Bhârata as a river, purifying all the worlds, to destroy the sins
of the inhabitants of Bhârata. Bhagiratha will take you there after
much entreating and worshipping you; and you will be famous by the
name Bhagirathî, the most sanctifying river in the world. There, the
Ocean born of my parts, and the King S'ântanu also born of my parts
will be your husbands. O Bharatî! Let you go also and incarnate in
part in Bhârata under the curse of Gangâ.
So, here the country Bharata Varsha is being referred to.