Out of the two types of streaming video we have Synchronous vs Asynchronous.
YouTube can utilize both modes. Instructors can either setup a live stream, or can record something offline and upload for students to access later.
Switcher Studio allows you to use iOS devices to switch camera views, add lower thirds and graphics to the live stream. You can set up using your ipad and some phones, and even add your laptop screen into the mix. The phones act as remote cameras and with the ipad you can switch between each of the cameras and even screen share your laptop. The feed from the switcher can then go to YouTube or Facebook Live, or some other 3rd party CDN.
Using a device such as the Blackmagic Web Presenter, you can add an SDI or HDMI camera into the mix by converting the signal into USB so any software looking for a web cam can see the camera. This enables a higher quality production since these cameras have a much larger imagining chip and much higher quality lens.
Many screen capturing software is available for instructors to capture what is happening on their screen. I often see instructors using the picture in picture mode, but this is very distracting for the student. Our brains our wired to look at faces, so the students attention is now in conflict between the face and what the instructor is trying to demonstrate. My suggestion would be to show your face while introducing the video, then switch completely back to the screen for what you want the students to see.
I prefer using Camtasia due to its robust and easy to use editing capabilities, TechSmith actually advertises it as a video editor. Many tools are built into the software to allow you to really highlight, zoom in, focus on the content you want your students to see. The following example was created by the instructor. He sent me his original Camtasia recordings and then I was able to edit the amount of screen he was showing. Originally he had captured his entire desktop and the portion that he was working on was a very small part of the overall screen, so by zooming in I have isolated just the content the students need to see.