I'm finding that Smart Matches are matching to the wrong person in mine and other's trees. As an example I have Phillis Bridge and Sarah Bridge in my tree. The Smart Matching is matching my Phyllis Bridge to Sarah Bridge in the other person's tree and Sarah Bridge from my tree to Phyllis Bridge in the other member's tree. The individual details are correct, it's the matching which is skewiff. It's happened on a number of occasions.
I found a lot of people that way!. Most people have 2 first names and many people find their second name nicer so change it. They are than known by a different first name than is recorded on their birth certificate and descendants without that piece of paper would not know. In your case there could be a girl called Philis Sarah Bridge or the other way around. It is worth investigating further or get in touch with the person from the other tree to see if it can be clarified. There are also lots of people with the same name and details, important to find out whom their parents are.
Happens all the time to me too. I am using Family Tree Builder; at first I used to reject the match where the Main Persons matched correctly but one or more of the family displayed in the 'Compare tree' were incorrectly matched.
Now, as I check new matches, I review the old ones. In all cases (many of them previously rejected) I confirm the match if the Main Person is the SAME PERSON in my tree and in the proposed match. Not just the name of course but matching dates of birth etc., and obviously not a different family, but if there are the sort of mismatches between other family members we have been talking about I still confirm the match. I have decided the system is about matching the main persons; if the others show up in their own SmartMatch as main person and don't match I will reject them then.
I have probably confused the hell out of the system by changing my criteria to what I now believe is correct, and in the process confirming previously rejected matches, but it will settle down!
I am not going to look it up now but I think the philosophy and method of SmartMatch use should be better (and SIMPLY) explained in the Manual and other guidance material. Especially that it is a proposed match between the Main Persons and that the others are just shown so that you can see that the family is the same, NOT to compare matches between other family members.