It is not the same concepts
Katalium is a framework that provides a blueprint for test automation projects based on Selenium and TestNG.
Katalon Studio is an automated testing tool.
If you need to work with TestNG and Selenium, go with Katalium, download the source and example code from the below links, open it with Visual Studio Code.
For simple explanation, Katalium is the blueprint, sample project that based on Selenium and TestNG.
If you need to work with Katalon Studio (testing tool), you can use Katalon Studio and open the example projects under the menu: File > New Sample Project
“how to write code in katalium framework in visual studio code” - as the above information, you can open Katalium project with Visual Studio Code and take a look, How to write it will require you to know about Selenium and TestNG.