The first version of ASP.NET came around 2001 as part of .NET Framework overcoming the challenges faced by classic ASP for Windows environment web development.
Since it's inception, millions of applications have been developed and new features have been added in each releases of ASP.NET (from ASP.NET 1 to ASP.NET 4.5). These features were making ASP.NET base classes heavy and lengthy.
The new ASP.NET Core has been developed completely from scratch; a complete new architecture has been used and that is the reason ASP.NET Core is much leaner, modular framework.
The famous and base
System.Web.dll is no more into ASP.NET Core as it is based on few set of granular and small packages from NuGet. So you no longer need to use a set of .dlls always in ASP.NET Core whether you need it or not. Just use only those .dlls that you need actually in your application (so light weight and simple). This helps ASP.NET Core application to become smaller, lighter, more secure, along with better peformance.
As against traditional ASP.NET, we no longer have ASP.NET Web Form, ASP.NET MVC, ASP.NET Web API. Its all in one.
Below are benefits of ASP.NET Core against traditional ASP.NET
What is this means? It means ASP.NET Core application is developed using MVC Pattern (you have no choice but to follow this pattern), so all the benefits of MVC patterns comes automatically with ASP.NET Core.