I am bit confused whether Bharatavarsha refers to the entire globe or only india. Because in the puranas sometimes some names of rivers or the mountains are unfamiliar and many times it also says bharatavarsha is divided into 9 parts. So I am just confused.
What my personal belief is - jambudvipa is continent , bharatvarsha is indian sub continent and bharat is south part of bharatvarsha that is india
from sanatkumara samhita
In the three worlds the most fortunate place is the earthly planets. The best of them is Jambudvīpa. In Jambudvīpa the best place is Bhārata-varṣa. In Bhārata-varṣa the best place is Mathurā-purī.
from Vishnu Purana
THE country that lies north of the ocean, and south of the snowy mountains, is called Bhārata, for there dwelt the descendants of Bharata. It is nine thousand leagues in extent, and is the land of works, in consequence of which men go to heaven, or obtain emancipation.The seven main chains of mountains in Bhārata are Mahendra, Malaya, Sahya, Śuktimat, Rikṣa, Vindhya, and Pāripātra.From this region heaven is obtained, or even, in some cases, liberation from existence; or men pass from hence into the condition of brutes, or fall into hell. Heaven, emancipation, a state in mid-air, or in the subterraneous realms, succeeds to existence here, and the world of acts is not the title of any other portion of the universe.The Varṣa of Bhārata is divided into nine portions, which I will name to you; they are Indra-dvīpa, Kaserumat, Tāmravarṇa, Gabhastimat, Nāga-dvīpa, Saumya, Gandharva, and Vāruṇa; the last or ninth Dvīpa is surrounded by the ocean, and is a thousand Yojanas from north to south.
From Brahmanda Puran
I shall recount to you all the subjects here in the Bhārata Varṣa.This is a mysterious sub-continent in the middle (of the universe) where the fruits (of Karimas) are enjoyed whether auspicious or mauspicious.The sub-continent that is to the north of the ocean as well as to the south of the Himavān, is called the sub-continent of Bhārata where the subjects are Bhāratī (pertaining to Bhārata).
From Brahma Purana
To the north of ocean and to the South of Himālayas is the sub-continent Bhārata. The subjects are called Bhāratis.O leading sages, its extent is nine thousand Yojanas. This is the land of holy rites to those who opt for heavenly pleasure and absolution.The seven Kulaparvatas are Mahendra, Malaya, Sahya, Śūktimān, Ṛkṣa, Vindhya and Pāriyātra .It is from here, O brahmins, that the heaven is attained; one attains absolution too from here, men attain the state of different species of animals or fall in hell from here alone.It is from here alone that men go to heaven or realize absolution at the end of their series of birth. Nowhere else on the earth are holy rites prescribed for men. Listen to the nine divisions of this sub-continent. The are Indradvīpa, Kaserumān, Tāmraparṇa, Gabhastimān, Nāgadvīpa, Saumya, Gāndharva and Vāruṇa.Bhārata, the ninth among them, is an island encircled by the ocean. This island extends from South to North a thousand Yojanas.
Listen, O brahmins, the Bhārata sub-continent has nine sub-divisions which are separated by oceans. They are equal to one another.They are Indradvīpa, Kaseru, Tāmravarṇa (? Tāmraparṇa), Gabhastimān, Nāgadvīpa, Saumya, Gandharva and Varuṇa. Bhārata surrounded by the ocean is the ninth among them. The island extends from south to north and is one thousand Yojanas long.In the east of it, the Kirātas stay. The Yavanas stay in the west. O brahmins, the Brahmins, Kṣatriyas, Vaiśyas and Śūdras stay in the middle.They are sanctified by holy rites and worldly pursuits as sacrifice, warfare, trading. Their general behaviour is intelligible through their activities, which cause heavenly pleasures and liberation. They incur merit and sin thereby.There are seven Kula mountains viz., Mahendra, Malaya, Sahya, Śūktimān, Ṛkṣa, Vindhya and Pāriyātra. There are thousauds of other mountains nearby. They are vast, lofty and beautiful. They are immense. Their ridges are of wonderful and variegated nature. They are Kolāhala, Vaibhrāja, Mandara, Dardala, Vātādhvaga, Daivata, Maināka, Surasa, Tuṅgaprastha, Nāga, Godhana, Pāṇḍura, Puṣpa, Vaijayanta, Raivata, Arbuda, Ṛṣyamūka, Gomantha, Kṛtaśaila, Śrī Cakora and hundreds of other mountains. The populated realms are interspersed with these mountains. The Mlecchas live in parts of this territory. Excellent waters of these rivers are drunk by those people. O excellent brahmins, know these rivers.The following rivers rise from the foot of the Himavān:—Gaṅgā, Sarasvatī, Sindhu, Candrabhāgā, Yamunā, Śatadrū, Vipāśā, Vitastā, Airāvatī, Kuhū, Gomatī, Dhūtapāpā, Bāhudā, Dṛṣadvatī, Devikā, Cakṣu, Niṣṭhīvā, Gaṇḍakī and Kauśikī.
From shiv purana
I shall explain the Bhāratavarṣa. South of the Himālaya mountain and north of the ocean is the land of Bharata. O great sage, its extent is nine thousand Yojanas. This is the land of sacred rites for attaining heaven and salvation. So say the wise people. Heaven and hell are attained by men from here only. I shall mention nine subdivisions of the Bhārata Varṣa to you.Indradyumna, Kaseru, Tāmravarṇa Gabhastimat, Nāgadvīpa, Saumya, Gandharva, Vāruṇa and the ninth is the sub-continent Sāgarasambhṛta. This sub-continent lies North to South extending to a thousand Yojanas.To the east of Bhārata live the Kirātas,to the south the Yavanas; to the west Khaśas and to the north the ascetics.In the middle live the Brahmins, Kṣatriyas, Vaiśyas and Śūdras maintaining themselves by sacrifices, battles, merchandise and service. There are seven Kulaparvatas viz Mahendra, Malaya, Sahya, Sudāmā, Ṛkṣaparvata, Vindhya and Pāriyātra.O sage, Vedas, Smṛtis, Purāṇas and other things issue from Pāriyātra. They dispel all sins, it should be known, by their very sight or touch.The great rivers issuing from Vindhya are seven, such as Narmadā, Surasā etc, and thousands of smaller ones are all auspicious. They quell all sins. Godāvarī, Bhīmarathī, Tāpī, and other important rivers issue from the mountain Ṛkṣa. They dispel fear of sins immediately.The rivers Kṛṣṇā Veṇī and others issue from Sahya Kṛtamālā, Tāmraparṇī and others issue from Malaya.Triyāmā, Ṛṣikulyā and others issue from Mahendra. Ṛṣikulyā, Kumārī and others issue from Śuktimat.
It refers only to India.
Said the God of fire: The country which lies to the north of the ocean and on the south side of the mount Himalaya is called Bharatvarsa and measure nine thousand yojanas in breadth. The country named above is the working place of those who ascend heaven or enjoy other celestial comforts by dint of their own piety and through the merit of good deeds done there in. The seven principal mountain chains (Kulaparvata) which traverse the continent of Bharatvarsa, are Mahendra, Malaya, Sahya, Suktiman, Hemaparvata (the Golden mountain), the Vindhya and the Pariyatra. The nine islands (territories in which the above said country is divided), are, Indradvipa, Kaseru, Tamravani, Gabhastiman, Nagadvipa, Saumya, Gandharva, Varuna and Ayam which are surrounded by all sides by the sea. The country above described is eight thousand miles in length from North to South and is divided into nine principal divisions named after the people residing therein and which lie around the central part of the country from the East. They are the land of the Kiratas, the land of the Yavanas, the land of the Brahmanas from whose lips drop down the deep and profound truths inculcated in the Vedas and Smritis. In mount Pariyatra is the source, of several rivers, while the Narmada and several other streams take rise from the Vindhya. The Tapi and the Payosnika, the Godavari, the Bhimarathi, the Krsna, the Veni and several other rivers take rise from the Sahya Mountain, while the Krtamala and the Trisama respectively floe from the Malaya and the Mahendra Mountains. The rivers Kumara and others have their source in the Suktiman Mountain, while the Candrabhaga takes its rise from the Himalaya. The countries known as the Kurupancala and the Madhya-desa are in the western part of the continent of India.
Agni Purana 119.1-8