Sanskrit is one language not many different. It is like saying Bavarian German aka High German is different language from Hamburg German - they are both German. So there is and will be difference between regular speakers with good grammar vs occasional speakers with poor grammar. I run in these issues when I speak basic Sanskrit with Gurukul based students.
The source of Sanskrit and Sanskrit influence is the Saraswat Valley civilisation around 6000 BC. Some recent books have done radio carbon, Sanskrit literature, astronomical charts, climatic events and genomics to validate the time line. The central Asian language influence is migration out of India to Central Europe & Volga referred to as Uttar Kuru.