I hope it is not true that most mathjobs postdoc ads are for "named postdocs", because these exist mostly at very elite places: I am not aware of more than a dozen of them altogether. Generally there are on the order of 100 postdocs you can apply for at mathjobs.
Anyway, mathjobs is quite good at separating out various kinds of positions. At my institution we currently have four different mathjobs ads including two different kinds of postdocs. Of course you need to read carefully and understand the differences among all these positions (not all of our applicants do so).
I can go in and look if you insist (really; it's not a problem), but I strongly suspect that if you are only finding "named postdocs" then you are not reading carefully enough and missing the other postdocs offered by the same departments. The vast majority of math postdocs really are available on mathjobs; I can't even think of another place that advertises these positions in any quantity.
It is possible, but I wouldn't assume so. Again, mathjobs allows you to tailor your application to multiple positions at the same place. For instance you may use the same recommendation letters but submit different cover letters, and you might submit a teaching statement for one position and not another.
If you have any questions about this, feel free to ask at the department of interest.
Added: Thanks to Noah Snyder, who pointed out that the "dozen" above is not accurate. In fact that is the answer to a different question, namely how many departments offer postdocs under the name "Firstname Lastname Assistant Professor". I would be interested to know which departments offer "named postdocs" of one kind or another. I think it is more than 12 and less than 50.
Actually, I just checked, and 36 out of the top 55 math departments have named postdocs. So probably there are about 50 altogether.