As to the other, I think the practical difference MIGHT be something like this: "We" go to the magisterium or the consensus patrum or whatever. We expect to find an authoritative and reliable statement. "They" go to the Bible, and have no expectation of an authoritative interpretation, and see no need for one. Further they expect that since even councils can err, that nothing is reliable outside Scripture. So the Church becomes an association of like-minded people, and fissparates frequently.
We have a greater stress on koinonia and tghe benefits of a visible communion. They teach an invisible Church of those who have made an appropriate appeal to the mercy of God in Christ and, presumably, don't doubt critical things like, say, "blood atonement".
My guess is that either they must appeal to an inner "assurance" or say it's unknowable whether one is in the True Church or not. We say it's easy to tell if one is in the true Church, but harder to know if one is going to go to heaven after one dies.
It's a package, I'm thinking, based around the turning away from the very idea of a magisterium.
I guess one could say, if every one is his own pope, then who says who gets to run services on Sunday? That is, one's entire approachc to the "Ecclesial assembly" will be different. What we think looks like Balogna, or worse, to them. What they think looks like anarchy and a systematic denial of the possiblity of epistemological certainty.
How'm I doing?
The Protestant response would be that they have that certainty in the big, e.g. in the four solas, and they don't need the certainty in the rest of the doctrine. Further, contrary to all scripture, they insist that sola scriptura and sola fide is plain in the scripture and needs no pope or magisterium. Apparently the Holy Ghost told them something He did not bother to put in writing, and left them meander in the desert looking for the rest.
That's an interesting way to put it, and I think you are being very fair. You made me think about what my actual expectation is when I read the Bible as far as authoritative interpretation. When I read a passage that I have never studied, and off the top of my head I can't relate it to anything else I do know about, you are absolutely right that I don't really put much weight on my own "gut feeling" about it.
So, I will check what other people I respect and who are more learned than I have said about it. Usually, those views are filled with other scripture in support of whatever the position is. It is only at that point that I might think to myself, "that position is authoritative". I claim that scripture interprets itself, so if a position has a great weight of scripture in support of it, I would claim it to be correct and authoritative.
You are absolutely right that we do not believe anything outside the Bible is authoritative, and we also believe that doesn't mean that anything outside the Bible is automatically wrong.
My guess is that either they must appeal to an inner "assurance" or say it's unknowable whether one is in the True Church or not. We say it's easy to tell if one is in the true Church, but harder to know if one is going to go to heaven after one dies.
A Reformer would say that it is absolutely knowable whether one himself is in the true Church, but that none of us can be certain about anyone else, even those in the same faith. This is all based on our interpretation of scripture. When I first said the sinner's prayer, I did not have 100% assurance that I was saved because I didn't have the background. It was only later when it was showed to me in scripture that I became sure, i.e. multiple verses on top of themselves supporting the literal take on John 3:16.