Hi,
ASP.NET WebParts were introduced in .NET 2.0 around 2005, they are similar idea but not compatible with Sharepoint WebParts. There was some talk of making them compatible way back when, but it never happened as far as I know.
Way back then I was kind of interested in ASP.NET WebParts when it first came out, so I implemented the MyPage feature in mojoPortal and made it possible to expose existing content in mojoPortal as WebParts. I thought also that a market for 3rd party ASP.NET WebParts would emerge as it did for Sharepoint WebParts, but it never caught on, there are no third party ASP.NET WebParts to speak of, and as a technology I think now ASP.NET WebParts are dead.
Best,
Joe