Can I create a webapplication on my windows 10 IOT running device
(R-PI 3)?
Yes, you can start with Hello blinky official sample. There are also Python and Node.js supported.
Using ASP.NET, you can publish Web Application on Windows IoT core. (Note the version of ASP.NET, more detailed information is here.)
And, restup is a HTTP server for universal windows platform (UWP) apps that can run on Raspberry Pi with Windows IoT core.
PS I added 2 tages: Windows IOT and Windows-10-IOT-Core.... are these
the same?
Windows IoT core is an edition of Windows 10 differs from desktop and mobile editions. It is optimized for smaller devices with limited resources, such as Raspberry Pi 2 and 3.
Window IoT is something about Internet of Things you can create with Windows.
For tags in SO, "Windows IoT core" and "Window IoT" have identical function.