The term Bhārata & Bhārata-Varṣa may be used interchangeably.
- Varṣa just means a "region" or a "division".
The Skanda Mahā-Purāṇa and the Agni Mahā-Purāṇa exactly mentions what constitutes the BhārataVarṣa.
1. Skanda Mahā-Purāṇa
Chapter 11, Prabhāsa-kṣetra-māhātmya, Skanda-purāṇa
ईश्वर उवाच ।
पृथिव्या मध्यगर्भस्थं जंबूद्वीपमिति स्मृतम् । तच्च वै नवधा भिन्नं
वर्षभेदेन सुन्दरि ॥ ६ ॥
Īśvara said:
- What is remembered as Jaṃbūdvīpa is exactly at the centre of the
earth. It is divided into nine regions, O beautiful woman, known as
the different Varṣas (regions).
तस्याद्यं भारतं वर्षं तच्चापि नवधा
स्मृतम् । नवयोजनसाहस्रं दक्षिणोत्तरमानतः ॥ ७ ॥
- Therein, the first Varṣa is Bhārata. It is also remembered as being
divided into nine parts. From south to north it measures nine thousand
Yojanas.
अशीतिश्च सहस्राणि पूर्वपश्चायतं स्मृतम् । उत्तरे हिमवानस्ति
क्षीरोदो दक्षिणे स्मृतः ॥ ८ ॥
- The distance from east to west is eighty thousand. Himavān is in the
north. The Kṣīroda (ocean) is in the south.
एतस्मिन्नंतरे देवि भारतं
क्षेत्रमुत्तमम् । कृतं त्रेता द्वापरं च तिष्यं युगचतुष्टयम् ॥ ९ ॥
अत्रैवैषा युगावस्था चतुर्वर्णश्च वै जनः । १०.क ।
- 9 to 10a. O goddess, Bhārata, the excellent Kṣetra, is in between. There
are four Yugas, viz. Kṛta, Tretā, Dvāpara and Tiṣya (i.e. Kali). The
division of Yugas exists only here. So also the classification of the
people into four Varṇas.
चत्वारि त्रीणि च द्वे च तथैवैक शरच्छतम् ॥ १०.
ख ॥ जीवन्त्यत्र नरा देवि कृतत्रेतादिषु क्रमात् । यदेतत्पार्थिवं पद्मं
चतुष्पत्रं मयोदितम् ॥ ११ ॥ वर्षाणि भारताद्यानि पत्राण्यस्य
चतुर्द्दिशम् । भारतं केतुमालं च कुरु भद्राश्वमेव च ॥ १२ ॥
- 10b. to 12. O goddess, the men here live upto four hundred, three
hundred, two hundred and one hundred years, in the Yugas Kṛta, Tretā
etc. respectively. I told you about the earth likened to a lotus with
four petals. The Varṣas Bhārata etc. are the petals in the four
quarters, viz. Bhārata, Ketumāla, Kuru and Bhadrāśva. भारतं नाम
यद्वर्षं दाक्षिणात्यं मयोदितम् । दक्षिणापरतो यस्य पूर्वेण च महोदधिः ।
हिमवानुत्तरेणास्य कार्मुकस्य यथा गुणः ॥ १३ ॥
- The southern-most Varṣa that has been mentioned by me by the name
Bhārata has oceans to its south, west and east. Himavān is to the
north like string unto bow.
English Translation by G.V. Tagare
Agni Purāṇa also ratifies the above Passages.
2. Agni Mahā-Purāṇa:
Chapter 118
अग्निरुवाच:
उत्तरं यत्समुद्रस्य हिमाद्रेश्चैव दक्षिणं ।
वर्षं तद्भारतं नाम नवसाहस्रविस्तृतं ॥१॥
Agni Said -
- That country which (lies) to the north of ocean and south of Himādri (Himālaya) is known as the Bhāratavarṣa extending to nine
thousand (yojanas).
English Translation by N. Gangadharan
So basically, most parts of the present day Indian Subcontinent - bounded by the great Himalayas in the North, the Arabic Sea in West, the Indian Ocean in the South, and the Bay of Bengal to the East, this portion in between these four bodies constitutes the BhārataVarṣa, as per the Skanda & the Agni Mahā-Purāṇa.
Bhārata & Bhārata-Varṣa are same as per the texts.
Politically, in the present day context, Bhārata refers to the Republic of India, as codified in the 1st Article of the Indian Constitution as -
Article 1.1 - "India, that is Bharat, shall be a union of states."