The scriptural name of Hinduism is Sanatan Vedic dharm. Vedas are the final authority on Hinduism.

Vedas proclaim that Shri Krishna is The Supreme God. Ved Vyas has explained that He appears mainly in three different forms, i.e. Brahm, Paramatma and Bhagavan.

The Shrimad Bhagawat Mahapuran asserts –

वदन्ति तत्त्तत्वविदस् तत्त्वं यज्ज्ञानमद्वयम् ।
ब्रह्मेति पर्मात्मेति भगवानिति शब्द्यते ॥
भा १.२.११
vadanti tatttatvavidas tattvaṁ yajjñānamadvayam ।
brahmeti parmātmeti bhagavāniti śabdyate ॥
bhā 1.2.11

"Those who know the Supreme Entity say that He has eternally existed in three forms - Brahm, Paramatma and Bhagavan".

Brahm

This formless appearance of Shri Krishna is known as Brahm (Devanagari: ब्रह्म ISO15919: brahma).

Each form of God possesses innumerable divine powers. Yet He does not reveal His name, divine form, leelas, attributes, abode and associates in this form. The only powers revealed in this form are He keeps His existence and is the invisible ocean of unlimited bliss. 

रूपं यत्तत्प्राहुरव्यक्त्तमाद्यं, ब्रह्मज्योतिर्निर्गुणं निर्विकारम्।
सत्तामात्रं र्निर्विशेषं निरीहं, सत्वं साक्षाद विष्णुरध्यात्म दीपः ॥
rūpaṁ yattatprāhuravyakttamādyaṁ, brahmajyotirnirguṇaṁ nirvikāram।
sattāmātraṁ rnirviśeṣaṁ nirīhaṁ, satvaṁ sākṣāda viṣṇuradhyātma dīpaḥ ॥

The gyanis worship Shri Krishna in this imperceptible form.

Paramatma

Lord MahaVishnu form of Shri Krishna is known as Paramatma (Devanagari: परमात्मा ISO15919: paramātmā).

Devotees in Vaikunth Lok, worship Lord MahaVishnu and sing His glories. These devotees do not enjoy physical proximity or a close relationship with Him.

Maha Vishnu is ever adorned with four arms. In each of His hands He holds a conch, disc, club and lotus. His permanent divine abode is Vaikunth Dham. He reveals His name, form, abode and attributes but does not exhibit any leelas or have any associates.

Vaikunth is a place of unlimited majesty. His divine form with four arms, the radiance (तेज​) and speed (गति) of His disc (सुदर्शन चक्र), the club (गदा) are constant reminders that He is omnipotent God.

Those who follow the path of Yoga and the devotees, who worship Lord Vishnu, go to divine abode of Vaikunth where they get a beautiful divine form (2) similar to that of Lord Maha Vishnu. In Vaikunth they respect Him and bask in His glory. But cannot have any closeness with Him.

Paramatma dwells in the hearts of all the living beings and witnesses all their actions. He also gives fruits of their actions. (1)

Bhagavan

The third form of Shri Krishna is known as Bhagavan (Devanagari: भगवान ISO15919: bhagavāna).

His divine abode is Golok. In this form Shri Krishna conceals His majesty. His divine majesty is called aishwarya (Devanagari: ऐश्वर्य ISO15919: ​aiśvarya) then descends on Earth in a human form with the sole purpose of distributing love to deserving souls.

He is endowed with names (Devanagari: नाम ISO15919: nāma), form(Devanagari: रूप ISO15919: rūpa), pastimes, attributes (Devanagari: गुण ISO15919: guṇa), abode (Devanagari: धाम​ ISO15919: dhāma) and His associates (Devanagari: परिकर ISO15919: parikara​).

In this form, the Supreme God hides His divinity and comes down to the level of the common man. Then He showers love abundantly on His devotees through ever-new fun-filled pastimes. His pastimes are most edifying as well. Thus, it is the sweetest form of God.

Therefore, worshiping this form is the easiest way to realize God. In this form devotees do not fear the aishwarya of Paramatma. Devotees who worship Lord Krishna in this form, do not need to walk the arduous path of Gyan Marg to reach the apex of renunciation (see Difference between the vairagya of gyani and bhakt). Those who worship this form of Bhagavana attain divine bliss and Golok Dham or Saket lok.

Examples of this form are Shri Krishna, Shri Ram.

Are all these form same?

It seems that Brahm, Paramatma and Bhagavan are the same. Are they?

Yes, just like water, ice and vapor are three forms of water  with different properties. Brahm, Paramatma and Bhagavan are different aspects of the same Brahm-Supreme God. Material water can exist in one state at any given time. Contrary to that all three aspects of God have coexisted since eternity.

Also, Their attributes are eternal too. 

चयस्विषामित्यवधारितं पुरा ततः शरीरीति विभाविताकृतिम्।
विभुर्विभक्तावयवं पुमान इति क्रमादमुन्नारद इत्यबोधि सः ॥शिशुपाल वध​

Once, in Dwarka, the courtiers in Shri Krishna’s palace saw a bright light descend from the skies. Everybody was curious to know what it was. As the light continued to descend further, a bright shape materialized. They presumed that a celestial god (devata) was descending, which made them happy. Soon they realized that it was Narad Ji, who they very warmly welcomed to their kingdom. This “light” form of God is comparable to the impersonal form, Brahma(ब्रह्म).

The Gyani (see Gyan) worships the Brahm form. They enjoy the Supreme God as a spot of light with no name (नाम), no form(रूप), no pastimes(लीला), no attributes (गुण), no abode (धाम) and no associates (परिकर).

Our mind is accustomed to focus on a form. With no visual form to meditate upon, following Gyan Marg becomes extremely difficult for aspirants.

निराधार मन चकृत धावे ।

Seeing a bright form the curiosity of the courtiers was replaced by eagerness to meet the devata. This is comparable to Paramatma. The yogis (see Yoga) worship and enjoy this divine form along with His names, attributes and abode.

When Saint Narad descended further and they could see him clearly, they were delighted to have his association. This is comparable to the form of Bhagavan.

When God descends on the earth in human form and plays, enjoys a meal and does all other things like a human, seeing Him in this form, no one can fathom that "He is God". It is in this form that other human beings can love Him freely.

This was the state of the inhabitants of Braj who never glorified Shri Krishna as Bhagavan-Shri Krishna. Having no inkling of His divinity they loved Him wholeheartedly like their friend, child and beloved.