There is only One Truth, but many ways to be confused. There are people of different levels of understanding, both students and teachers, some closer to truth and some farther. This is why there are different explanations and different teachings - all partially valid in different ways.
When you know Truth, you can see: this teaching is partially valid from this side but wrong here; and this other teaching does a better job explaining this piece but has a problem with this other thing. When you know Truth you can see how it all connects. But when you don't know Truth these different perspectives seem contradicting. But they are not contradicting, what's missing is your understanding of Truth.
It's like with 3D objects, there may be multiple flat projections drawn on paper, each is a partially valid representation of the object - but each is ultimately wrong. When you know the 3D object, you can see how these projections relate to it - but if you don't know the object, the projections seem completely unrelated, nothing in common. Dharma is like this, even more complex than a single 3D object.
Specifically about stopping unskillful states, Buddha said that there is suffering (=bad experience) and that suffering can be stopped (=no more bad experience). He then said that the cause of suffering are unskillful mindstates, esp. craving, but also anger, fear, torpor, doubt, ignorance etc. He also said that suffering can be stopped through getting rid of these unskillful mind states and generating skilful mindstates. The culmination of this process is Nibbana. Are we good so far?
So, if it were impossible to get rid of unskillful mind states, it would be impossible to stop suffering. If that were the case, there wouldn't be any Buddhism, it would be pointless to try. But Buddhism exists.
Now, there are two schools of thought as to how the unskillful mindstates can be removed. These two schools of thought are two different flat projections of the same 3D object. They are two simplifications.
One school of thought says, we should make effort to actively get rid of unskillful mindstates. So if we have anger, we should stop it, when we have lust we should stop it and so on. The idea here is, if we don't make effort to fix the problem it won't go away by itself.
The other school of thought says, that just looking at the mind directly is enough to remove the unskillful states. The idea here is, unskillful mindstates appear when we think about some external objects and form some sort of attitudes toward them like craving or rejection. But if we look at our mind directly without judgement, in that very moment there is no attitude of craving or rejection, so right at that moment there is peace.
In reality, the two methods are the same method. In both cases we do something to stop the unskillful mindstate. In both cases we stop feeding it, by no longer thinking about the external object or problem, we take our attention from it. It's just that in one case we talk about the old thing we're stopping but not what we do instead, and in the other case we talk about the new thing we are doing (looking at mind directly) without mentioning the fact that by doing that we're stopping to feed the bad thought. So we are just talking about two sides of the same elephant. The actual practice is the same.
Now, about labeling. Labeling is just a way to switch your mind from thinking about the problem to looking at the mind. That's all. There is no magic value in labeling other then helping you switch your attention. If you can switch your attention to mind without labeling, then you don't need to label. It's like training wheels on the bike.
However, the problem with labeling is, some people tend to obsess with the label itself too much, instead of looking at the mind which is the whole point. This is why I always say, don't overdo it, it's not about labels it's about the mind.
It's like, when you look at the sunset standing on a cliff over the ocean, and someone calls you on the phone and asks what you see, and you just say "sunset". Isn't that a horrible vulgarization of the actual experience? Squeezing the entire endless ocean, colors, wind, and the atmosphere to a single label? Similarly, when you are labeling what happens in your mind. You are simplifying something subtle, deep, and nuanced - something alive - to a single label, a dead concept of logical mind. The danger there is, if you keep labeling it, at some point you will stop paying attention to the colors and wind and the background sounds - because you will know: it is "sunset". That's it. Once you know it you no longer see it. That's the danger with labeling in meditation, as well as post-meditation practice. Makes sense?
So you can either actively stop the bad mindstates by shifting attention away from them, or you can simply look at your mind, and in both cases you may use labels or not - as long as you know what you are doing and why, the practice is essentially the same.
As you can see, when you understand what's going on, there is no conflict between different schools or methods. They just approach it from different sides. The Truth is one and the same.