Personally, I would put the "line" between a Skeptical Doubter and a Faithful Doubter as the emphasis on the adjective/noun relationship in each phrase. In other words, a skeptical believer is a believer, first and foremost. The skepticism is a characteristic of the believer. A faithful doubter, on the other hand, is a doubter, first and foremost. The faithful is a characteristic of the doubter.
To make this real and practical, try the following:
If someone makes a claim or a statement that sounds different than what you believe, what is your first reaction - your "gut instinct"? If it is to accept that there is some validity in it and then look for that validity - even if you have to discard some of it to find it, you are a skeptical believer. You believed there was good in there somewhere, and you were willing to exercise skepticism to sort through the incorrect to find the good.
If, however, your immediate reaction is, "That's a bunch of crap," you are less likely to search through it for a nugget of gold. You still are "faithful" to what you believe, but you aren't very open to finding insights among the ashes - to wade through the grime to find the sublime. Your "faithfulness" keeps you anchored to your current truth, but it keeps you anchored away from any other truth.
(Btw, I think you can be a temple-recommend holding Mormon and be a faithful doubter - or an atheist and a skeptical believer. Neither title automatically endows one or the other with any degree of "truth". That is a completely separate discussion.)