I think that for me the problem, is that, as a child you learned something over time, starting with the basics, slowly learning the ever more complicated details, constantly reinforcing the correct information, as you go on. It's like when I learned French, I must have studied it, on and off for about 12 years, and though I never use it, and am now 44 years post school, I can still pick up a book, or magazine and make some sense of it, though my memory of vocabulary is poor!!
In Genetic Genealogy, there is no 'gg for dummies' - you jump right in, reading about highly complicated topics and principles, and you do understand - but someone ask you about a closely related topic, and you realise how narrow your area of understanding is! I am forever suddenly questioning myself, re my understanding of bits of information, that I assumed were right, but - well maybe not!!
Anyway, that's enough of my 'mature woman's confidence issues'!! On to this specific subject!
So, the basics, as you say are that you share, say 100 cM , over say 9 segments. Depending on the company, that may be only segments over a minimum size, and it may be the cM's making up those segments. Or it may be the total cM's, whatever the size of any of the segments you have in common. So you share those amounts with him/her, and they share the same amounts with you. You would be matching for the cM's & segments given, if you could compare your DNA on a chromasome browser, the one Ancestry doesn't have!!
Your joint matches are a different kettle of fish. What I think is that you both have to have matches with any 'joint' match, but I don't know whether these have to be the same matches, or if you could have a match on Ch 1, and the other party matches the third individual on CH22, would that still constitute a joint match?
One of the reasons fore my sore head, is that I have just discovered a low level match, who by comparison with a'gold standard' match on my paternal side, I had allocated to my paternal side - easy yeh!! and yet 90 minutes later, I find him matched to a 'gold standard' match on my maternal side. I would say that, though I am from the great Irish diaspora, on both sides, I have never found any evidence that they had 'met' before, until both sets of Grandparents moved to my parents and my birthplace, just before my parents were born.
So, anybody with 'Genetic Genealogy for Dummies' - I'll pay a fair price!!