How to record from websites ?

I have some classes that I would like to record on various websites.
It seems easy to record from streaming services, but other websites it is not so clear how to do it. 
I had Audials years ago, and I think I just copied and pasted urls.

I have tried this:
Record / Video Streaming
Other Source / Screen Recording
Direct Video Recording
Web Browser / Firefox
Record
A new browser window opens and the prompt box changes to 
Play a video on Record one video in Firefox
No recording happens.  

I have not yet tried screen recording because I would prefer that the video be recorded and not force me to watch it at the same time :)
Thanks for your help!