Custom controls:

A control authored by a user or a third-party software vendor that does not belong to the .NET Framework class library. This is a generic term that includes user controls. A custom server control is used in Web Forms (ASP.NET pages). A custom client control is used in Windows Forms applications.

User Controls:

In ASP.NET: A user-authored server control that enables an ASP.NET page to be re-used as a server control. An ASP.NET user control is authored declaratively and persisted as a text file with an .ascx extension. The ASP.NET page framework compiles a user control on the fly to a class that derives from the System.Web.UI.UserControl class.