What is the difference between the God and an Avatara?

 a) God

God is an English Word adopted by others.

The original term to indicate the formless ENERGY that creates, governs the Universe is BRAHMAN - ब्रह्मन्. And, occasionally, Indra, Saraswati, etc, are mentioned in Rig Veda as BRAHMA, the formless BRAHMAN/God.

Rig Veda 2.41.18 (Saraswati)

इमा ब्रह्म सरस्वति जुषस्व वाजिनीवति । या ते मन्म गृत्समदा ऋतावरि प्रिया देवेषु जुह्वति ॥
imā brahma sarasvati juṣasva vājinīvati | yā te manma gṛtsamadā ṛtāvari priyā deveṣu juhvati ||

English translation:

Enjoy these sacred formulations here, o BRAHMAN Sarasvatī rich in prize-winning mares, the thoughts dear to the gods that the Gr̥tsamadas pour for you, the embodiment of ṛtam (The cosmic Truth).

b) Avatara or incarnation

In Sanskrit, the word avatara has the following meanings:

1. to descend
2. Physical manifestation/descending on the Earth of a Physical God, viz., Vishnu, Shiva, Devi, etc, as a human/animal

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Rig Veda, which is the source of all types of spiritual concepts for subsequent literature like Brahmanas/Puranas, contains the word avātiratam - avatṛ, to indicate keeping down/eliminating/descending, but does not contain the 2nd concept of Physical manifestation as a human/animal.

Rig Veda 1.152.1

युवं वस्त्राणि पीवसा वसाथे युवोरच्छिद्रा मन्तवो ह सर्गाः । अवातिरतमनृतानि विश्व ऋतेन मित्रावरुणा सचेथे ॥
yuvaṃ vastrāṇi pīvasā vasāthe yuvor acchidrā mantavo ha sargāḥ | avātiratam anṛtāni viśva ṛtena mitrāvaruṇā sacethe ||

English translation:

You two wear garments of fat; your counsels are unbroken torrents. You have brought low all untruths; you keep company with truth.

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There is no concept of Avatara or incarnation in Sanatana Dharma.