I think I have found the core of your difficulties.
When I talk about liberals in the Church .. I mean what you have described.
When I talk about Modernists in the Church, I mean the really bad guys.
You need to forget about the scale. There is no scale.
A "Modernist" is not merely a "really bad liberal". There isn't a scale with "liberal, bad liberal, really bad liberal and modernist". Liberalism isn't just a mild case of Modernism.
Modernism is a heresy. One that was described very clearly and aggressively and successfully opposed by Pope Pius X. If you put "Modernism" and "Pius X" into Google you will be able to read what the definition is. You will immediately recognise the liberals of our acquaintance, those people who are now in charge of the Church around the world. It is a creed opposed to that of the Catholic Church. The thing that makes people like Gumbleton and Sr. Joan and Cardinal Mahoney, et al, "liberals" is the heresy called Modernism. How much of a liberal (as the term is commonly used in the Catholic media) you are depends on how much of the Modernist creed you willingly and consciously adhere to and how much Catholicism you have retained. The two things are opposed and where one is ascendant, the other will be suppressed. You can't be a Modernist Catholic.
Now, from the point of view of a Trad like me, nearly all the people who are regarded as "conservatives" in the Church right now are to one degree or another infected, mostly unconsciously, with Modernism. But they mostly don't have enough knowledge of the Faith to know it. This situation has been created by the corruption of the Church hierarchy. People have not been taught the Faith, but Modernism instead, as you and I both know. They are Modernists, but it isn't their fault, and if you told them, (when they were finished being mad at you) they would do their best to stop being Modernists.
Perhaps that is the real distinction between a "liberal" and a "conservative" ; merely that a "liberal" is a Modernist on purpose. He is someone who has consciously agreed to the tenets of Modernism and has willingly abandoned the Faith in favour of it.
A "conservative" is someone who really wants to be a Catholic, who would reject any heresy if it were presented to him as such because he wants to do the will of God in good faith. He is a Modernist but only because he knows no better. If he is one, it is because one day in the late 1960s, the Church "woke and groaned to find itself Modernist". He is, therefore, consciously opposed to, and often actively engaged in fighting "liberalism" in the Church. He is at war with Modernism, even if he doesn't know it, and doesn't know how much he himself is infected with it.
Which is why "conservative" Neo-Catholics like S--- are so angry with us Trads. Why they hate us so much is that we have learned how much Modernism has infiltrated the Church and have rejected it and are in the process of fighting it in ourselves and outside, just as he is, but we can see it in him and he can't. (I'm sorry if this sounds insufferable, but I can't help it. If you are a Trad, you will, by definition, be able to see things that non-Traditionalist Catholics can't. Unfortunately, because Trads are all fallen, it does indeed tend to make us insufferable.)
We see that he too is suffering from the Modernist infiltration. Trads want the Neos to come out of the Modernist matrix. But because the Catholic Real is so much more frightening than the Catholic Real, they can't face and react with anger at the people who are trying to get them out. (Again, I disclaim here: a lot of Trads are just pests and it is perfectly reasonable to get mad at them, but there are a few of us who really really do want to see all the poor Neos released from the prison of the Matrix.)
Very few modern Catholics know half of what the Church teaches, and if they did, it would scare them silly. Don't forget, most of them, even the "conservatives" think that feminism can be "Christianised," that it is natural and good for Church and State to be separated, that "freedom of speech" is a natural human right... a lot of rubbish, but it is rubbish upon which their entire universe is founded. It is no wonder, then, that they are scared stiff of the fullness of the Faith and get angry with Trads and call us names when we point out that they are infected with the Disease. (That and I think I mentioned Trads tend to be jerks about it.)
But imagine his position, for a moment. He wants to be a good Catholic, thinks he is being a good Catholic by accepting all the tenets of the Faith he has been told about, and by fighting the bad guys, the "liberal Catholics" who have infiltrated the Church. He thinks he is doing the will of God and working for the right side. And he is, by virtue of his good intentions and the mercy of God.
Then along come the Trads and say things like, "Oh yeah? Well, what about the Social Reign of Christ the King?"
"The what of whom?" they respond.
"Don't you know that the separation of Church and state were condemned by the Popes?"
No. He doesn't. He has never been told this in his life.
Imagine what his reaction would be. He gets his entire self-image threatened, his total self-understanding as being one of the Good Guys, along with having his entire social and political foundation yanked out from under him. He is then presented with the awful reality of just how bad everything really is in the world and the Church, and it turns out to be a hell of a lot worse than any conservative is capable of imagining on his own. No longer is he the good guy fighting a good and more or less winnable fight. Now he is himself a compromiser, a collaborator, who adheres to a set of anti-Catholic proposals in a world that is totally howling mad and rapidly turning into hell on earth.
Really, is that a club you'd want to join? I'd get mad at that messenger, wouldn't you?
(That, and the Trads tend to be jerks about it...)
A Neo-Catholic conservative is someone who loves the faith, who wants to be as Catholic as possible, but in large part has not been given enough information.
(I believe this is the default position of nearly everyone in the Church who still more or less believes what the Church teaches and wants to do the right thing. I have reservations, however, about a lot of people who have set themselves up as Professional Catholics, writing on the net about the faith as apologists or amateur theologians who write "popularising" books about Catholicism, their conversions to it and who go on lecture tours making money as a "conservative Catholic" celebrity. Once you have that much professional stake in a position, it is going to be very, very difficult to change it when you discover its limitations. This is the main reason I object to the whole world of "professional Catholicism" that you find a lot of in the US. But really, this is neither here nor there for this purpose today. In general, I believe in the good will of "conservatives".)
Many, many times, when he fully understands how untenable his position is, he changes it. And that is how many of us have become Trads. We learned about all this hidden stuff about the Faith, we learned what has really been happening in the Church and the world. We then went through an incredibly painful transition period where we learned all sorts of awful things about how the Church is nearly destroyed, and we had a big personal crisis. Sometimes we ran off and join up with the SSPX or some other schismatics or do-it-yourselfers.
If we are given to emotional or psychological instability, if wen were alone and had no one around to help, we might have a really really bad time of things and gone a little bonkers (which is why a lot of Trads are jerks). But most of us settle down, remember that God is God and owns the Church, and will work things out in His own way and that our job is to be as faithful as possible in the given circumstances. After that, we generally settle in to whatever we are doing in life, whether it is raising a family, doing our jobs or whatever, find a decent place to go to the Old Mass, and get on with life.
Understand all this, and you will have a much easier time sorting out your terminology.