.NET Core is a version of .NET Framework (first versions were released in the summer of 2016) that denotes a major breakthrough in the Microsoft Development Technologies ecosystem, the greatest promise being its ability to execute cross-platform: Windows, MacOS, and Linux.
Besides, .NET Core is modular, open source, and cloud-ready. It can be deployed along with the application itself, minimizing installation issues.
Although the number was consecutive to previous versions initially, Microsoft decided to restart the numbering, reinforcing the idea that this is a totally new concept with respect to classical versions, as a better way to avoid ambiguities. For those who were already aware of the initial versions, let's remember that the equivalence is as follows (refer to the screenshot):
The screenshot shows the equivalence between the new names and how some technologies go beyond platforms and (as it happens in ASP.NET Core or MVC Core) can even execute over the classic platform...