You have spoken 100% correctly about these two cases, in line exactly with what the scholars of ḥadīth and usool say.
But there remains a third case, and it is the most common case - when it can not be confirmed specifically (textually) in that ḥadīth who was doing the ordering. As in the ḥadīth when 'Aa'ishah said regarding menstruating women, "We were ordered to make up our days of fasting, but we were not ordered to make up our prayers." (Bukhārī and Muslim)
Insha'Allaah, I think it would be best to compile notes based only on the course. Wikipedia etc. are not credible sources, it is an online encyclopedia which is not credible, it contains factual and unfounded claims which often can't be seperated. Amongst the non-Muslims, it is heavily criticised for its credibility and accuracy. As for us Muslims, we would likely be more concerned especially as it relates to info posted on Islam. As for other external links, one would need to ascertain that those people and or publications are from trustworthy credible sources. I think in this case, the goal was to complete the document from the course (and notes from last year's course - see
May Allaah reward you all for your wonderful efforts masha'Allaah! The response to the Summer Course Forum has been great and shows how much love everyone has for seeking knowledge and contributing towards khair.
One thing I forgot (about wikipedia), I know a brother who tried to clean up the information on ad-da'watus-salafiyyah on the site, was able to post some good info. Later, it was deleted and replaced with nonsense by the moderator who is evidently from the shee'ah. Since the person was a senior moderator, she was able to remove all his info and replace it with lies. That's wikipedia, the online encyclopeida-blog.
Wow Mashallah, Jazakalalh for pointing all this amazing information out as well as my mistakes. Please do correct them and forgive me. I realy did not know about all the little extra info. My intention was to find a clear concise simple enough definition for the glossary. Some places I still feel confused. Maybe I need a visual, because its not clear. I forgot to check over regarding the sallá Allāhu ʿalayhi wa-sallam, astighfirullah. I intend for future to keep it from course material only inshallah.