I have recently been looking into different apologetic methods and from what I’ve noticed, presuppositionalism and the moral argument seem to have a lot of similarities. Would you agree or am I misunderstanding something?
You're right, as others have pointed out. One of the biggest misunderstandings of Van Til's method is that it only applies to one thing, logic or science. But that's wrong, the Transcendental Argument is an awkward way of phrasing it because no one pays attention to what is after that phrase.
It's usually phrased as "The Transcendental Argument from (fill in the blank)". That "blank" is anything and everything in theory. That's because "transcendental" is a method of argumentation, rather than a set argument used the same way every time (now there's no shortage of internet individuals who use it that way "By What Standard" and all that).
Bahnsen in his "Van Til: Reader" describes it as a method first and foremost, the section on TA I believe. Then in his application of the method (that he's famous for) he applies it to areas he thinks are easier for the average Christian to understand. But those are only specific applications of the method to specific things we experience, like morality for one.
James Anderson has also applied the same method to other areas, some a little more complex (though Bahnsen was quite at home in the weeds of technical philosophical thinking) than how Bahnsen applied it.
Why the difference if it's only about one thing? Because it's not a static argument but a method of argumentation that can be applied to all of human experience. So each Apologist applies it to their own areas of expertise.
Bahnsen and Anderson apply it to more epistemological issues because that's their area of primary expertise. But Christopher Watkins applies the same method to contemporary French philosophy because that's his area of expertise. And on and on it goes.
Someone like William Edgar applies it to art and beauty among other issues because that's his area of expertise. That's the beauty of the method. It's tailored in a sense to the individual but as wide in application as creation itself.
So yes there's overlap between the TA and the moral argument as you and others have pointed out. In fact Immanuel Kant, the father of transcendental argumentation, famously had the moral argument for God applying that method.
If you view the Transcendental Argument as one fixed and static argument about one thing and then notice that "hey that's a lot like this argument, so I wonder if there's overlap" then you're right. But the problem is in how you conceived or thought about what kind of argument it is.
Classical Apologetics has a particular method of argumentation and therefore has arguments from causality, order, and the other "Five Ways" of Aquinas (or how those "Ways" have been developed). The TA can be applied to the same things but with a different structure of argument.
So the difference is in the structure of the type of arguments used not so much the data. Even Evidentiary Apologetics is a method applied to different types of evidence for something like the resurrection for instance. Van Til's method is applying a different type of analysis of the same evidence in a different way (exposing the bias and therefore different conclusions based on one's Worldview). But it's still just two different methods being applied to the same "evidence".
I hope my rambling comments help make more sense of the situation on top of the already useful responses given. If anything I said is confusing to anyone then please feel free to call me on it and I'll attempt to explain better.