No, they are not the same.
Chanakya who is also called Kautilya who lived around 4th century BCE. He wrote a work on politics and economics with the name Artha shastra based on the works of ancient teachers.
From English translation of Kautilya's Artha Shastra by Shama Shastry
This Arthasástra is made as a compendium of almost all the Arthasástras, which, in view of acquisition and maintenance of the earth, have been composed by ancient teachers.
So, it is clear that there were other Artha shastras before the time of Chanakya. He only took the name Artha shastra because it discusses topics like politics, economics, duties of a king.
In the ancient India, students were taught 64 arts and 14 sciences arts. Artha shastra was also taught because it is an Upaveda. It is one of the 14 sciences.
The Mimamsâs, Tarka, Samkhya, Vedanta, Yoga, Itihasas, Puranas, Smritis, theory of Sceptics, Artha Sâstra, Kama shastra, Silpa Sstra, Alañkâra (Rhetoric), Kavyas, language of the folk (vernacular), the art of spenking properly, the theory of Yavanas, and manners and customs of countries and nations—these are the thirty-two Vidyâs.
Now, this Artha shastra is not the same as the one written by Kautilya. Kautilya lived around 4th century BCE. Krishna and Balarama lived very much older to that. These sciences were also present during the time of Ramayana. We will find some principles of politics, strategies in the Valmiki Ramayana also.
vīrāḥ ca niyatotsāhā rāja śāstram anuṣṭhitāḥ |
śucīnām rakṣitāraḥ ca nityam viṣaya vāsinām || 1-7-12
They are valiant ones with engineered enthusiasm, administrators of political science, clean persons and protectors of subjects of their kingdom at all times.
iṣu astra vara sampannam artha śāstra viśāradam |
sudhanvānam upādhyāyam kaccit tvam tāta manyase || 2-100-14
"O, my darling! I hope that you treat with due respect; Sudhanva, your teacher in archery, who is furnished with the most excellent arrows and darts and well-versed in political economy."
So, it is clear that there was artha shastra before Chanakya. The one he wrote is a collection of various artha shastras from ancient times. That doesn't make Kautilya's Artha shastra a Hindu scripture. It is just a treatise on political economy based on previous artha shastras.